ELECTROMANETISM ♦ TSTU PUBLISHING HOUSE ♦ Ministry of Education of the Russian Federation TAMBOV STATE TECHNICAL UNIVERSITY ELECTROMANETISM Laboratory work Tambov TSTU Publishing House 2002 M. Savelyev, Yu. P. Lyashenko, V. A. Shishin, V. I. Barsukov E45 Electromagnetism: Lab. slave. / A. M. Savelyev, Yu. P. Lyashenko, V. A. Shishin, V. I. Barsukov. Tambov. Publishing House Tamb. state tech. un-ta, 2002. 28 p. Guidelines and descriptions of laboratory facilities used in the performance of three laboratory works on the section of the course of general physics "Electromagnetism" are presented. In each work, a theoretical substantiation of the corresponding methods for experimentally solving the problems posed, as well as a methodology for processing the results obtained, is given. Laboratory work is intended for 1st-2nd year students of all specialties and forms of engineering education. UDC 535.338 (076.5) BBK В36Я73-5 © Tambov State Technical University (TSTU), 2002 Educational publication ELECTROMAGNETISM Laboratory work Compiled by: Alexander Mikhailovich Savelyev, Yury Petrovich Lyashenko, Valery Anatolyevich Shishin, Vladimir Ivanovich Barsukov Editor and technical editor M. A. Ev seycheva Computer prototyping by M. A. F ilatova Signed for publication on 16.09.02. Format 60×84/16. Times NR headset. Newsprint paper. Offset printing. Volume: 1.63 arb. oven l.; 2.00 ed. l. Circulation 100 copies. C 565M Publishing and Printing Center of the Tambov State Technical University 392000, Tambov, st. Sovetskaya, 106, k. 14 CONTROL QUESTIONS 1 The physical meaning of the concepts of induction and magnetic field strength. 2 Write down the Biot-Savart-Laplace law and show its application to the calculation of the direct current field and the field on the axis of a circular current-carrying coil. 3 Derive calculation formulas for the field of a solenoid of finite length. 4 Explain the physical meaning of the theorem on the circulation of the magnetic field induction vector and its application to calculate the field of an infinitely long solenoid. 5 Explain the principle of operation, installation scheme and measurement technique. 6 How will the distribution of the field along the axis of the solenoid change depending on the ratio between its length and diameter? List of Recommended Readings 1 Savelyev IV Course of general physics. T. 2. M., 1982. 2 Detlaf A. A., Yavorsky B. M. Course of physics. M., 1987. 3 Akhmatov A. S. et al. Laboratory practice in physics. M., 1980. 4 Irodov IE Basic laws of electromagnetism. M.: Higher school, 1983. Laboratory work DETERMINATION OF THE SPECIFIC CHARGE OF AN ELECTRON "BY THE MAGNETRON METHOD" The purpose of the work: to get acquainted with the method of creating mutually perpendicular electric and magnetic fields, the movement of electrons in such crossed fields. Experimentally determine the magnitude of the specific charge of an electron. Devices and accessories: electronic lamp 6E5S, solenoid, power supply VUP-2M, milliammeter, ammeter, voltmeter, potentiometer, connecting wires. Guidelines One of the experimental methods for determining the specific charge of an electron (the ratio of the electron charge to its mass e / m) is based on the results of studies of the motion of charged particles in mutually perpendicular magnetic and electric fields. In this case, the trajectory of motion depends on the ratio of the charge of the particle to its mass. The name of the method used in the work is due to the fact that a similar movement of electrons in magnetic and electric fields of the same configuration is carried out in magnetrons - devices used to generate powerful electromagnetic oscillations of ultrahigh frequency. The main regularities explaining this method can be revealed by considering, for simplicity, the motion of an electron flying at a speed v into a uniform magnetic field, the induction vector of which is perpendicular to the direction of motion. As is known, in this case, the maximum Lorentz force Fl = evB acts on the electron when it moves in a magnetic field, which is perpendicular to the electron velocity and, therefore, is a centripetal force. In this case, the movement of an electron under the action of such a force occurs along a circle, the radius of which is determined by the condition: mv 2 evB = , (1) r where e, m, v are the charge, mass and speed of the electron, respectively; B is the value of the magnetic field induction; r is the radius of the circle. Or mv r= . (2) eB It can be seen from relation (2) that the radius of curvature of the electron motion trajectory will decrease with the increase in the magnetic field induction and increase with the growth of its velocity. Expressing the value of the specific charge from (1) we obtain: e v = . (3) m rB From (3) it follows that to determine the ratio e / m, it is necessary to know the speed of the electron movement v, the value of the magnetic field induction В and the radius of curvature of the electron trajectory r. In practice, to simulate such a motion of electrons and determine the indicated parameters, one proceeds as follows. Electrons with a certain direction of movement velocity are obtained using a two-electrode electron tube with an anode made in the form of a cylinder, along the axis of which a filamentous cathode is located. When a potential difference (anode voltage Ua) is applied in the annular space between the anode and the cathode, a radially directed electric field is created, under the action of which the electrons emitted from the cathode due to thermionic emission will move rectilinearly along the anode radii and the milliammeter included in the anode circuit, will show a certain value of the anode current Ia. A uniform magnetic field perpendicular to the electric, and hence the speed of the electrons, is obtained by placing the lamp in the middle part of the solenoid so that the axis of the solenoid is parallel to the axis of the cylindrical anode. In this case, when current Ic is passed through the solenoid winding, the magnetic field that arises in the annular space between the anode and cathode bends the rectilinear trajectory of the electrons. As the solenoid current Ic increases and, consequently, the magnitude of the magnetic induction B, the radius of curvature of the electron's trajectory will decrease. However, at small values ​​of the magnetic induction B, all the electrons that previously reached the anode (at B = 0) will still fall on the anode, and the milliammeter will record the constant value of the anode current Ia (Fig. 1). At some so-called critical value of magnetic induction (Bcr), the electrons will move along trajectories tangent to the inner surface of the cylindrical anode, i.e. already cease to reach the anode, which leads to a sharp decrease in the anode current and its complete cessation at values ​​B >< Bкр В = Bкр В > Bcr b a C Fig. 1. The ideal (a) and real (b) discharge characteristics of an electron are continuously changing due to the acceleration imparted to it by the forces of the electric field. Therefore, the exact calculation of the electron trajectory is rather complicated. However, when the anode radius ra is much larger than the cathode radius (ra >> rk), it is believed that the main increase in the electron velocity under the action of an electric field occurs in the region close to the cathode, where the electric field strength is maximum, and hence the greatest acceleration imparted to the electrons . The further path of the electron will pass almost at a constant speed, and its trajectory will be close to a circle. In this regard, at a critical value of the magnetic induction Bcr, the radius of curvature of the electron motion trajectory is taken as a distance equal to half the anode radius of the lamp used in the installation, i.e. ra rkr = . (4) 2 The speed of an electron is determined from the condition that its kinetic energy is equal to the work expended by the electric field to communicate this energy to it mv 2 = eU a , (5) 2 where Uа is the potential difference between the anode and cathode of the lamp. SUBSTITUTING THE VALUES OF THE VELOCITY FROM (5), THE RADIUS OF THE TRAJECTORY RKR FROM (4) INTO (3) AT THE CRITICAL VALUE OF THE INDUCTION OF THE MAGNETIC FIELD, WE GET THE EXPRESSION FOR THE RATIO e / m IN THE FORM: e 8U = 2 a2 . (6) m ra Bcr An improved calculation taking into account the cathode radius (rc) gives the relation for determining the specific charge of an electron e 8U a = . (7) m  r2  ra 2 Bcr 2 1 − k2   r   a  For a solenoid of finite length, the value of the critical magnetic field induction in its central part should be calculated by the formula (8) 4 R 2 + L2 where N is the number of turns of the solenoid; L, R are the length and average value of the radius of the solenoid; (Ic)cr. is the solenoid current corresponding to the critical value of the magnetic induction. Substituting Bcr in (7) we obtain the final expression for the specific charge 8U a (4 R 2 + L2) e = . (9) 2 2 rk 2  m µ 0 ra (I c) cr N 1 − 2  2  r   a  e. dependence of the anode current on the solenoid current Iа = ƒ(Ic). It should be noted that, in contrast to the ideal fault characteristic (Fig. 1, a), the real characteristic has a less steep falling part (Fig. 1, b). This is explained by the fact that electrons are emitted by a heated cathode with different initial velocities. The velocity distribution of electrons during thermal emission is close to the known law of Maxwell's velocity distribution of molecules in a gas. In this regard, the critical conditions for different electrons are reached at different values ​​of the solenoid current, which leads to a smoothing of the curve Iа = ƒ(Ic). Since, according to the Maxwell distribution, most of the entire flow of electrons emitted by the cathode has an initial velocity close to the probable one for a certain cathode temperature, the sharpest drop in the reset characteristic is observed when the solenoid current reaches the critical value (Ic)cr for this particular group of electrons . Therefore, to determine the value of the critical current, the method of graphical differentiation is used. For this purpose, the dependence ∆I a = f (I c) ∆I c is plotted on the graph of the dependence Iа = ƒ(Ic) at the same values ​​of the solenoid current. ∆Ia is the increment of the anode current with a corresponding change in the solenoid current ∆Ic. ∆I a An approximate view of the discharge characteristic Ia = ƒ(Ic) (a) and the function = f (I c) (b) is shown in fig. 2. The value of the critical current ∆I c ∆I a of the solenoid (Ic)cr, corresponding to the maximum of the curve = f (I c) , is taken to calculate Bcr according to formula (8). ∆I c Ia Ia Ic a b (Ic)cr Ic 2. Reset (a) and differential (b) characteristics of the lamp DESCRIPTION OF THE INSTALLATION THE INSTALLATION IS ASSEMBLED ON A 6E5C LAMP WHICH IS USUALLY USED AS AN ELECTRONIC INDICATOR. THE INSTALLATION ELECTRICAL DIAGRAM IS PRESENT IN FIG. 3. THE LAMP IS SUPPLIED WITH DC CURRENT FROM THE VUP-2M RECTIFYER, WHERE THE VOLTAGE VALUE BETWEEN THE ANODE AND CATHODE IS REGULATED WITH THE HELP OF A CIRCULAR POTENTIOMETER (ON THE FACE SIDE OF THE KNOB 0 ... 100 V). THE LAMP CATHODE IS HEATED BY AC VOLTAGE WITH VOLTAGE ~ 6.3 V REMOVED FROM THE RECTIFIER TERMINALS. THE RECTIFIER IS CONNECTED TO A 220 V MAINS SOCKET INSTALLED ON THE LABORATORY BELT. RICE. 3. INSTALLATION ELECTRICAL DIAGRAM: VUP-2M + R ~ 220V 10 - 100 V - V A ~ 6.3V VUP-2M - RECTIFIER; R - POTENTIOMETER 0 ... 30 OM; A - AMMETER 0 ... 2A; MA - MILLIAMMETER - 0 ... 2 MA; V - VOLTMETER 0 ... 100 V The solenoid L through the potentiometer R is powered from a DC source, connected to a ± 40 V socket, also mounted on a laboratory table. The solenoid current is measured with an ammeter with limits of 0 ... 2 A, the anode current is recorded with a milliammeter with limits of 0 ... 2 mA, and the anode voltage is recorded with a voltmeter with limits of measurement of 0 ... 150 V. PROCEDURE AND PROCESSING OF THE RESULTS diagram of fig. 3. On the measuring instruments, set the appropriate limits of the measured values ​​and determine the division value of each of them. 2 Connect the VUP-2M rectifier to the 220 V socket, and the outputs of the potentiometer R to the +40 V socket. Check the lamp glow output to the rectifier terminals ~6.3 V. the anode voltage values ​​specified by the teacher (U a1). 4 At zero current in the solenoid, note the maximum value of the anode current (Iа)max. Then, using the potentiometer R, increase the current in the solenoid (Ic) after a certain interval (for example, ∆Ic = 0.1 A), each time fix the value of the anode current. Take at least 15 ... 18 measurements. Enter the obtained values ​​of Ic and Ia in the table. 1. Tables 1 – 3 anode current, ∆Ia of the solenoid, ∆Ic (A) Current increment Solenoid current, Ic Increment Anode current Ia e (mA) (mA) ∆I a (A) No. (Ic)cr Bcr m p / n ∆I c (A) (T) (C/kg) Anode - cathode voltage U a 1 1: 18 Anode - cathode voltage U a2 1: 18 Anode - cathode voltage U a3 1: 18 5 Set another specified voltage on the voltmeter (U a 2) and repeat all the operations in paragraph 4. Enter the new data in the table. 2. Carry out similar measurements for voltage (U a3), and enter the measurements obtained in Table. 3. 6 For each value of the anode voltage, plot the graphical dependencies Iа = ƒ(Ic). On the same charts ∆I a, plot the dependences of the derivative of the anode current (dIa) on the solenoid current, i.e. = f (I c) and from them determine the critical ∆I c values ​​of the solenoid current (Ic)cr, as schematically shown in fig. 2. 7 Substitute the found values ​​(Ic)cr into formula (8) and evaluate the values ​​of the critical induction (Bcr) of the magnetic field for all values ​​of the anode voltage. 8 Using formulas (7) and (9), calculate the three values ​​of the specific charge of an electron (e / m)1,2,3. Find its average value and compare with the table value. 9 Calculate the relative error in determining the desired value (e / m) using the formula: (I c) cr 2 ∆ N 2 ∆ rk ∆ RR + ∆ LL + . + 2 2 + R +L N rk The values ​​of R, L, N, ra, rk are given on the installation, and take their errors according to the known rules for constant values. The errors ∆µ0 and ∆N can be neglected. Errors (∆Ic)cr and ∆Ua determine according to the accuracy class of the ammeter and voltmeter. 10 Based on the relative error, find the absolute error ∆(e / m), enter all calculated values ​​in the table. 1 – 3, and give the final result as e m = (e m) cf ± ∆ (e m) . 11 Analyze the results and draw conclusions. Test questions 1 Under what conditions is the trajectory of a charged particle in a magnetic field a circle? 2 Tell us about the installation device and the essence of the "magnetron method" for determining the specific charge of an electron. 3 What is the critical current of the solenoid, the critical value of the magnetic induction? 4 Explain the trajectories of electrons from the cathode to the anode at the solenoid current Ic< Iкр, Ic = Iкр, Ic > Icr. 5 Derive formula (6) and (8). 6 Explain the fundamental difference between the ideal and real reset characteristics of a vacuum tube. List of Recommended Readings 1 Savelyev IV Course of general physics. T. 2. M.: Nauka, 1982. 2. A. A. Detlaf, B. M. Yavorsky, et al. Course of Physics. Moscow: Higher school, 1989. 3 Buravikhin V.A. et al. Practicum on magnetism. M.: Higher school, 1979. 4 Maysova N.N. Workshop on the course of general physics. M.: Higher school, 1970. Laboratory work STUDY OF OWN ELECTROMAGNETIC OSCILLATIONS IN THE CONTOUR The purpose of the work: to study the influence of the parameters of the oscillatory circuit on the nature of the electromagnetic oscillations that occur in it, as well as the acquisition of skills in processing graphic information. Devices and accessories: an electronic generator of short-term rectangular pulses, periodically charging the circuit capacitor, a system of capacitors of various capacities, a battery of series-connected inductors, a set of resistors, an electronic oscilloscope, a Wheatstone bridge, switches, keys. Guidelines In an electric oscillatory circuit, periodic changes in a number of physical quantities (current, charge voltage, etc.) occur. A real oscillatory circuit in a simplified form consists of a capacitor C, an inductor L and active resistance R connected in series (Fig. 1). If the capacitor is charged and then the key K is closed, then electromagnetic oscillations will occur in the circuit. The capacitor will begin to discharge and an increasing current and a magnetic field proportional to it appear in the circuit. An increase in the magnetic field leads to the appearance of self-induction in the EMF circuit: CONTROL QUESTIONS 1 The physical meaning of the concepts of induction and magnetic field strength. 2 Write down the Biot-Savart-Laplace law and show its application to the calculation of the direct current field and the field on the axis of a circular current-carrying coil. 3 Derive calculation formulas for the field of a solenoid of finite length. 4 Explain the physical meaning of the theorem on the circulation of the magnetic field induction vector and its application to calculate the field of an infinitely long solenoid. 5 Explain the principle of operation, installation scheme and measurement technique. 6 How will the distribution of the field along the axis of the solenoid change depending on the ratio between its length and diameter? List of Recommended Readings 1 Savelyev IV Course of general physics. T. 2. M., 1982. 2 Detlaf A. A., Yavorsky B. M. Course of physics. M., 1987. 3 Akhmatov AS et al. Laboratory practice in physics. M., 1980. 4 Irodov IE Basic laws of electromagnetism. M.: Higher school, 1983. Laboratory work DETERMINATION OF THE SPECIFIC CHARGE OF AN ELECTRON "BY THE MAGNETRON METHOD" The purpose of the work: to get acquainted with the method of creating mutually perpendicular electric and magnetic fields, the movement of electrons in such crossed fields. Experimentally determine the magnitude of the specific charge of an electron. Devices and accessories: electronic lamp 6E5S, solenoid, power supply VUP-2M, milliammeter, ammeter, voltmeter, potentiometer, connecting wires. Guidelines One of the experimental methods for determining the specific charge of an electron (the ratio of the electron charge to its mass e / m) is based on the results of studies of the motion of charged particles in mutually perpendicular magnetic and electric fields. In this case, the trajectory of motion depends on the ratio of the charge of the particle to its mass. The name of the method used in the work is due to the fact that a similar movement of electrons in magnetic and electric fields of the same configuration is carried out in magnetrons - devices used to generate powerful electromagnetic oscillations of ultrahigh frequency. The main regularities explaining this method can be revealed by considering, for simplicity, the motion of an electron flying at a speed v into a uniform magnetic field, the induction vector of which is perpendicular to the direction of motion. As is known, in this case, the maximum Lorentz force Fl = evB acts on the electron when it moves in a magnetic field, which is perpendicular to the electron velocity and, therefore, is a centripetal force. In this case, the movement of an electron under the action of such a force occurs along a circle, the radius of which is determined by the condition: mv 2 evB = , (1) r where e, m, v are the charge, mass and speed of the electron, respectively; B is the value of the magnetic field induction; r is the radius of the circle. Or mv r= . (2) eB It can be seen from relation (2) that the radius of curvature of the electron motion trajectory will decrease with the increase in the magnetic field induction and increase with the growth of its velocity. Expressing the value of the specific charge from (1) we obtain: e v = . (3) m rB From (3) it follows that to determine the ratio e / m, it is necessary to know the speed of the electron movement v, the value of the magnetic field induction В and the radius of curvature of the electron trajectory r. In practice, to simulate such a motion of electrons and determine the indicated parameters, one proceeds as follows. Electrons with a certain direction of movement velocity are obtained using a two-electrode electron tube with an anode made in the form of a cylinder, along the axis of which a filamentous cathode is located. When a potential difference (anode voltage Ua) is applied in the annular space between the anode and the cathode, a radially directed electric field is created, under the action of which the electrons emitted from the cathode due to thermionic emission will move rectilinearly along the anode radii and the milliammeter included in the anode circuit, will show a certain value of the anode current Ia. A uniform magnetic field perpendicular to the electric, and hence the speed of the electrons, is obtained by placing the lamp in the middle part of the solenoid so that the axis of the solenoid is parallel to the axis of the cylindrical anode. In this case, when current Ic is passed through the solenoid winding, the magnetic field that arises in the annular space between the anode and cathode bends the rectilinear trajectory of the electrons. As the solenoid current Ic increases and, consequently, the magnitude of the magnetic induction B, the radius of curvature of the electron's trajectory will decrease. However, at small values ​​of the magnetic induction B, all the electrons that previously reached the anode (at B = 0) will still fall on the anode, and the milliammeter will record the constant value of the anode current Ia (Fig. 1). At some so-called critical value of magnetic induction (Bcr), the electrons will move along trajectories tangent to the inner surface of the cylindrical anode, i.e. already cease to reach the anode, which leads to a sharp decrease in the anode current and its complete cessation at B > Bcr. The form of the ideal dependence Iа = ƒ(B), or the so-called reset characteristic, is shown in fig. 1 dash-dotted line (a). The same figure schematically shows the trajectories of electrons in the space between the anode and cathode for different values ​​of the magnetic field induction B. It should be noted that in this case, the trajectories of electrons in the magnetic field are no longer circles, but lines with a variable radius of curvature. This is because the speed Ia A K B=0 V< Bкр В = Bкр В > Bcr b a C Fig. 1. The ideal (a) and real (b) discharge characteristics of an electron are continuously changing due to the acceleration imparted to it by the forces of the electric field. Therefore, the exact calculation of the electron trajectory is rather complicated. However, when the anode radius ra is much larger than the cathode radius (ra >> rk), it is believed that the main increase in the electron velocity under the action of an electric field occurs in the region close to the cathode, where the electric field strength is maximum, and hence the greatest acceleration imparted to the electrons . The further path of the electron will pass almost at a constant speed, and its trajectory will be close to a circle. In this regard, at a critical value of the magnetic induction Bcr, the radius of curvature of the electron motion trajectory is taken as a distance equal to half the anode radius of the lamp used in the installation, i.e. ra rkr = . (4) 2 The speed of an electron is determined from the condition that its kinetic energy is equal to the work expended by the electric field to communicate this energy to it mv 2 = eU a , (5) 2 where Uа is the potential difference between the anode and cathode of the lamp. SUBSTITUTING THE VALUES OF THE VELOCITY FROM (5), THE RADIUS OF THE TRAJECTORY RKR FROM (4) INTO (3) AT THE CRITICAL VALUE OF THE INDUCTION OF THE MAGNETIC FIELD, WE GET THE EXPRESSION FOR THE RATIO e / m IN THE FORM: e 8U = 2 a2 . (6) m ra Bcr An improved calculation taking into account the cathode radius (rc) gives the relation for determining the specific charge of an electron e 8U a = . (7) m  r2  ra 2 Bcr 2 1 − k2   r   a  For a solenoid of finite length, the value of the critical magnetic field induction in its central part should be calculated by the formula (8) 4 R 2 + L2 where N is the number of turns of the solenoid; L, R are the length and average value of the radius of the solenoid; (Ic)cr. is the solenoid current corresponding to the critical value of the magnetic induction. Substituting Bcr in (7) we obtain the final expression for the specific charge e 8U a (4 R 2 + L2) = . (9) 2 2 m 2  2 µ 0 ra (I c) cr N 1 − rk   r2  a  . dependence of the anode current on the solenoid current Iа = ƒ(Ic). It should be noted that, in contrast to the ideal fault characteristic (Fig. 1, a), the real characteristic has a less steep falling part (Fig. 1, b). This is explained by the fact that electrons are emitted by a heated cathode with different initial velocities. The velocity distribution of electrons during thermal emission is close to the known law of Maxwell's velocity distribution of molecules in a gas. In this regard, the critical conditions for different electrons are reached at different values ​​of the solenoid current, which leads to a smoothing of the curve Iа = ƒ(Ic). Since, according to the Maxwell distribution, most of the entire flow of electrons emitted by the cathode has an initial velocity close to the probable one for a certain cathode temperature, the sharpest drop in the reset characteristic is observed when the solenoid current reaches the critical value (Ic)cr for this particular group of electrons . Therefore, to determine the value of the critical current, the method of graphical differentiation is used. For this purpose, the dependence ∆I a = f (I c) ∆I c is plotted on the graph of the dependence Iа = ƒ(Ic) at the same values ​​of the solenoid current. ∆Ia is the increment of the anode current with a corresponding change in the solenoid current ∆Ic. ∆I a An approximate view of the discharge characteristic Ia = ƒ(Ic) (a) and the function = f (I c) (b) is shown in fig. 2. The value of the critical current ∆I c ∆I a of the solenoid (Ic)cr, corresponding to the maximum of the curve = f (I c) , is taken to calculate Bcr according to formula (8). ∆I c Ia Ia Ic a b (Ic)cr Ic 2. Reset (a) and differential (b) characteristics of the lamp

Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education "Voronezh State Forest Engineering Academy" PHYSICS LABORATORY PRACTICE MAGNETISM VORONEZH 2014 2 UDC 537 F-50 Published by the decision of the educational and methodological council of the FGBOU VPO "VGLTA" Biryukova I.P. Physics [Text]: lab. workshop. Magnetism: I.P. Biryukova, V.N. Borodin, N.S. Kamalova, N.Yu. Evsikova, N.N. Matveev, V.V. Saushkin; Ministry of Education and Science of the Russian Federation, FGBOU VPO "VGLTA". - Voronezh, 2014. - 40 p. Managing editor Saushkin V.V. Reviewer: Cand. Phys.-Math. Sciences, Assoc. Department of Physics VGAU V.A. Beloglazov The necessary theoretical information, description and procedure for performing laboratory work on the study of terrestrial magnetism, the Lorentz force and the Ampère force, and the determination of the specific charge of the electron are given. The device and principle of operation of an electronic oscilloscope are considered. The textbook is intended for students of full-time and part-time forms of study in areas and specialties, the curricula of which provide for a laboratory workshop in physics. 3 CONTENTS Laboratory work No. 5.1 (25) Determination of the horizontal component of the induction of the Earth's magnetic field ………………………………………………………………………… 4 Laboratory work No. 5.2 (26) Determination of magnetic induction …………………………………………. 12 Laboratory work No. 5.3 (27) Determination of the specific charge of an electron using a cathode ray tube …………………………………………………………………. 17 Laboratory work No. 5.4 (28) Determination of the specific charge of an electron using an indicator lamp ……………………………………………………………………….... 25 Laboratory work № 5.5 (29) Study of the magnetic properties of a ferromagnet ………………………. 32 APPENDIX 1. Some physical constants .............................................................. ................ 38 2. Decimal prefixes to the names of units ............……………………. 38 3. Symbols on the scale of electrical measuring instruments ..................... 38 Bibliographic list .................................. ............................................. 39 Lab #5.1 (25) DETERMINATION OF THE HORIZONTAL COMPONENT OF THE EARTH'S MAGNETIC FIELD INDUCTION Purpose of the work: study of the laws of the magnetic field in vacuum; measurement of the horizontal component of the induction of the Earth's magnetic field. THEORETICAL MINIMUM Magnetic field A magnetic field is created by moving electric charges (electric current), magnetized bodies (permanent magnets), or a time-varying electric field. The presence of a magnetic field is manifested by its force action on a moving electric charge (conductor with current), as well as by the orienting effect of the field on a magnetic needle or a closed conductor (frame) with current. Magnetic induction Magnetic induction B is a vector, the module of which is determined by the ratio of the maximum moment of forces Mmax acting on the loop with current in a magnetic field to the magnetic moment pm of this loop with current M B = max . (1) pm The direction of the vector B coincides with the direction of the normal to the loop with the current, which is established in the magnetic field. The magnetic moment pm of the frame with current modulo is equal to the product of the current strength I and the area S, bounded by the frame pm = IS. The direction of the vector p m coincides with the direction of the normal to the frame. The direction of the normal to the frame with current is determined by the rule of the right screw: if the screw with the right thread is rotated in the direction of the current in the frame, then the translational motion of the screw will coincide with the direction of the normal to the plane of the frame (Fig. 1). The direction of the magnetic induction B also shows the northern end of the magnetic needle, which is established in the magnetic field. The SI unit for magnetic induction is the tesla (T). 2 Biot-Savart-Laplace law Each element dl of a conductor with current I creates at some point A a magnetic field with induction dB, the magnitude of which is proportional to the vector product of the vectors dl and the radius vector r drawn from the element dl to a given point A (Fig. 2 ) μ μI dB = 0 3 , (2) 4π r where dl is an infinitesimal element of the conductor, the direction of which coincides with the direction of the current in the conductor; r is the modulus of the vector r ; μ0 is the magnetic constant; μ is the magnetic permeability of the medium in which the element and point A are located (for vacuum μ = 1, for air μ ≅ 1). dB is perpendicular Vector of the plane in which the vectors dl and r are located (Fig. 2). The direction of the vector dB is determined by the rule of the right screw: if the screw with a right-hand thread is rotated from dl to r in the direction of a smaller angle, then the translational motion of the screw will coincide with the direction dB. The vector equation (2) in scalar form defines the modulus of magnetic induction μ μ I dl sinα dB = 0 , (3) 4π r 2 where α is the angle between the vectors dl and r . The principle of superposition of magnetic fields If a magnetic field is created by several conductors with current (moving charges, magnets, etc.), then the induction of the resulting magnetic field is equal to the sum of the inductions of the magnetic fields created by each conductor separately: B res = ∑ B i . i Summation is performed according to the rules of vector addition. Magnetic induction on the axis of a circular conductor with current Using the Biot-Savart-Laplace law and the principle of superposition, one can calculate the induction of the magnetic field created by an arbitrary conductor with current. To do this, the conductor is divided into elements dl and, using formula (2), the induction dB of the field created by each element at the considered point in space is calculated. The induction B of the magnetic field created by all 3 conductors will be equal to the sum of the inductions of the fields created by each element (since the elements are infinitesimal, the summation is reduced to calculating the integral over the length of the conductor l) B = ∫ dB. (4) l As an example, let's define the magnetic induction at the center of a circular conductor with current I (Fig. 3a). Let R be the radius of the conductor. In the center of the coil, the vectors dB of all elements dl of the conductor are directed in the same way - perpendicular to the plane of the coil in accordance with the rule of the right screw. The vector B of the resulting field of the entire circular conductor is also directed at this point. Since all elements dl are perpendicular to the radius vector r, then sinα = 1, and the distance from each element dl to the center of the circle is the same and equal to the radius R of the coil. In this case, equation (3) takes the form μ μ I dl . dB = 0 4 π R2 Integrating this expression over the length of the conductor l in the range from 0 to 2πR, we obtain the magnetic field induction in the center of the circular conductor with current I . (5) B = μ0 μ 2R Similarly, one can obtain an expression for magnetic induction on the axis of a circular conductor at a distance h from the center of the coil with current (Fig. 3,b) B = μ0 μ I R 2 2 (R 2 + h 2) 3 / 2. EXPERIMENTAL TECHNIQUE (6) 4 The earth is a natural magnet, the poles of which are located close to the geographic poles. The Earth's magnetic field is similar to the field of a direct magnet. The magnetic induction vector near the earth's surface can be decomposed into horizontal B Г and vertical B B components: B Earth = В Г + В В. If a magnetic needle (for example, a compass needle) can freely rotate around a vertical axis, then under the influence of the horizontal component of the Earth's magnetic field, it will be installed in the plane of the magnetic meridian, along the direction B G. If another magnetic field is created near the arrow, the induction B of which is located in horizontal plane, then the arrow will turn through a certain angle α and will be set in the direction of the resulting induction of both fields. Knowing B and measuring the angle α, we can determine BG. A general view of the installation, called a tangent galvanometer, is shown in fig. 4, the electrical circuit is shown in fig. 5. In the center of the circular conductors (turns) 1 is a compass 2, which can be moved along the axis of the turns. The current source ε is located in housing 3, on the front panel of which are located: key K (network); potentiometer knob R, which allows you to adjust the current in the circular conductor; milliammeter mA, which measures the current strength in the conductor; switch P, with which you can change the direction of the current in the circular conductor of the tangent galvanometer. Before starting measurements, the magnetic needle of the compass is installed in the plane of circular turns in the center (Fig. 6). In this case, in the absence of current in the coils, the magnetic needle will show the direction of the horizontal component B G of the induction of the Earth's magnetic field. If you turn on the current in a circular conductor, then the induction vector B of the field created by it will be perpendicular to B G. The magnetic needle of the tangent galvanometer will turn through a certain angle α and will be set in the direction of the resulting field induction (Fig. 6 and Fig. 7). The tangent of the angle α of the deflection of the magnetic needle is determined by the formula 5 tgα = From equations (5) and (7) we obtain BГ = B . BG (7) μo μ I . 2 R tgα In a laboratory installation for increasing the magnetic induction, a circular conductor consists of N turns, which, according to the magnetic action, is equivalent to an increase in the current strength by N times. Therefore, the calculation formula for determining the horizontal component of the SH of the induction of the Earth's magnetic field has the form μ μIN BG = o . (8) 2 R tgα Instruments and accessories: laboratory stand. ORDER OF PERFORMANCE OF WORK The scope of work and the conditions for conducting the experiment are set by the teacher or a variant of an individual task. Measurement of the horizontal component of the SH of the Earth's magnetic field 1. By turning the body of the device, make sure that the magnetic needle is located in the plane of the coils. In this case, the plane of the turns of the tangent galvanometer will coincide with the plane of the magnetic meridian of the Earth. 2. Turn potentiometer R to the leftmost position. Set the K (network) key to the On position. Switch P put in one of the extreme positions (in the middle position of switch P, the circuit of turns is open). 3. Turn the potentiometer R to set the first set value of the current I (for example, 0.05 A) and determine the angle α1 of the pointer deviation from the initial position. 6 4. Change the direction of the current by switching switch P to the other extreme position. Determine the angle α 2 of the new arrow deflection. Changing the direction of the current allows you to get rid of the error caused by inaccurate coincidence of the plane of the turns with the plane of the magnetic meridian. Enter the measurement results in the table. 1. Table 1 No. of measurement I, A α1 , deg. α 2 , deg. α , deg B G, T 1 2 3 4 5 Calculate the average value of α using the formula α + α2 α = 1 . 2 5. The measurements indicated in paragraphs 3 and 4, carry out at four different values ​​of the current in the range from 0.1 to 0.5 A. 6. For each value of the current according to the formula (8), calculate the horizontal component B G of induction the earth's magnetic field. Substitute the average value α in the formula. The radius of the circular conductor R = 0.14 m; the number of turns N is indicated on the installation. The magnetic permeability μ of air can be approximately considered equal to unity. 7. Calculate the average value of the horizontal component B G of the induction of the Earth's magnetic field. Compare it with the table value B Gtabl = 2 ⋅ 10 −5 T. 8. For one of the values ​​of the current strength, calculate the error Δ B G = ε ⋅ B G and write down the resulting confidence interval B G = (B G ± ΔB G) Tl. Relative error in measuring the quantity B Г ε = ε I 2 + ε R 2 + εα 2 . Calculate the relative partial errors using the formulas 2Δ α ΔI ΔR ; εR = ; εα = εI = , I R sin 2 α where Δ α is the absolute error of the angle α, expressed in radians (to convert the angle α into radians, multiply its value in degrees by π and divide by 180). 9. Write a conclusion in which - compare the measured value B G with the table value; – write down the resulting confidence interval for the value B G; 7 - indicate which measurement of the quantities made the main contribution to the error in the value of B G. Studying the dependence of magnetic induction on the current strength in the conductor 10. To complete this task, follow steps 1 to 5. Record the measurement results in Table. 2. Table 2 No. of measurement I, A α1 , deg. α 2 , deg. α , deg Vexp, T Vtheor, T 1 2 3 4 5 11. Using the tabular value of the value B Гtabl = 2 ⋅ 10 −5 T, for each value of the current strength, using formula (7), calculate the experimental value of the induction Vexp of the magnetic field created by the coils . Substitute the average value α in the formula. Enter the results in table. 2. 12. For each current value, use the formula μ μI N (9) Btheor = o 2R to calculate the theoretical value of the magnetic field induction created by the turns. The radius of the circular conductor R = 0.14 m; the number of turns N is indicated on the installation. The magnetic permeability μ of air can be approximately considered equal to unity. Enter the results in table. 2. 13. Draw a coordinate system: the abscissa axis is the current strength I in the turns, the ordinate axis is the magnetic induction B, where construct the dependence of Vexp on the current strength I in the turns. Do not connect the obtained experimental points with a line. 14. On the same graph, depict the dependence of Vtheor on I by drawing a straight line through the points of Vtheor. 15. Estimate the degree of agreement between the obtained experimental and theoretical dependences B(I). Name possible reasons for their discrepancy. 16. Write a conclusion in which indicate whether the experiment confirms the linear dependence B(I); – whether the experimental values ​​of the induction of the magnetic field created by the coils coincide with the theoretical ones; indicate possible reasons for the discrepancy. 17. The compass of the tangent galvanometer can move perpendicular to the plane of the turns. By measuring the deflection angles α of the magnetic needle for various distances h from the center of the turns at a constant current strength I in the turns and knowing the value of B G, one can verify the validity of the theoretical formula (6). 8 CONTROL QUESTIONS 1. Expand the concepts of magnetic field, magnetic induction. 2. What is the Biot-Savart-Laplace law? 3. How is the direction and on what quantities does the magnetic induction in the center of a circular current-carrying conductor depend? 4. What is the principle of superposition of magnetic fields? How is it used in this work? 5. How is the magnetic needle installed a) in the absence of current in the turns of the tangent galvanometer; b) when current flows through the turns? 6. Why does the position of the magnetic needle change when the direction of the current in the turns changes? 7. How will the magnetic needle of the tangent galvanometer be installed if the installation is shielded from the Earth's magnetic field? 8. For what purpose is not one, but several tens of turns used in a tangent galvanometer? 9. Why, when conducting experiments, the plane of the turns of the tangent galvanometer must coincide with the plane of the Earth's magnetic meridian? 10. Why should a magnetic needle be much smaller than the radius of the turns? 11. Why does carrying out experiments with two opposite directions of current in the turns increase the accuracy of measuring B G? What experimental error is eliminated in this case? References 1. Trofimova, T.I. Physics course. 2000. §§ 109, 110. 12 Laboratory work No. 5.2 (26) DETERMINATION OF MAGNETIC INDUCTION Purpose of the work: study and verification of Ampère's law; study of the dependence of the induction of the magnetic field of an electromagnet on the strength of the current in its winding. THEORETICAL MINIMUM Magnetic field (see p. 4) Magnetic induction (see p. 4) Ampère's law Each element dl of a conductor with current I, located in a magnetic field with induction B, is affected by a force dF = I dl × B. (1) The direction of the vector dF is determined by the cross product rule: the vectors dl , B and dF form the right triple of vectors (Fig. 1). The vector dF is perpendicular to the plane containing the vectors dl and B . The direction of the Ampere force dF can be determined by the rule of the left hand: if the magnetic induction vector enters the palm, and the outstretched four fingers are located in the direction of the current in the conductor, then the thumb bent 90 ° will show the direction of the Ampere force acting on this element of the conductor. The Ampère force modulus is calculated by the formula dF = I B sin α ⋅ dl , where α is the angle between the vectors B and dl . (2) 13 EXPERIMENTAL TECHNIQUE The Ampère force in the work is determined using weights (Fig. 2). A conductor is suspended on the balance beam, through which current I flows. To increase the measured force, the conductor is made in the form of a rectangular frame 1, which contains N turns. The lower side of the frame is located between the poles of the electromagnet 2, which creates a magnetic field. The electromagnet is connected to a DC source with a voltage of 12 V. The current I EM in the electromagnet circuit is regulated by a rheostat R 1 and measured by an ammeter A1. The voltage from the source is connected to the electromagnet through terminals 4, located on the balance case. The current I in the frame is created by a 12 V DC source, measured by an ammeter A2 and regulated by a rheostat R2. Voltage is supplied to the frame through terminals 5 on the balance case. Through the conductors of the frame, located between the poles of the electromagnet, the current flows in one direction. Therefore, the Ampère force acts on the lower side of the frame F = I lBN , (3) where l is the length of the lower side of the frame; B - magnetic field induction between the poles of the electromagnet. If the direction of the current in the frame is chosen so that the Ampere force is directed vertically downwards, then it can be balanced by the gravity of weights placed on the pan 3 of the balance. If the mass of weights is m, then their force of gravity is mg and, according to formula (4), magnetic induction mg . (4) B= IlN Instruments and accessories: apparatus for measuring Ampere force and magnetic field induction; weights set. 14 ORDER OF PERFORMANCE OF WORK The scope of work and the conditions for conducting the experiment are set by the teacher or a variant of an individual task. 1. Make sure that the electrical circuit of the installation is assembled correctly. On rheostats R 1 and R 2 the maximum resistance must be entered. 2. Before starting measurements, the balance must be balanced. Access to the weighing pan is only through the side door. The balance is released (removed from the cage) by turning handle 6 to the OPEN position (Fig. 1). The scales should be handled with care; after the end of the measurements, turn knob 6 to the CLOSED position. 3. Inclusion of installation in a network is made by the teacher. 4. Fill in the table. 1 characteristics of electrical measuring instruments. Table 1 Instrument name Instrument system Measurement limit Ammeter for measuring current strength in a frame Ammeter for measuring current strength in an electromagnet = 0.5 g). Using rheostat R 1, set the current in the electromagnet circuit of the desired value (for example, I EM \u003d 0.2 A). 6. Release the balance and, using the rheostat R 2, select such a current I in the frame so that the balance balances. The results obtained are recorded in Table 2. Table 2 No. of measurement I EM, A t, g I, A F, N 1 2 3 4 5 7. At the same value of I EM, carry out four more measurements indicated in paragraph 5, each time increasing the mass of weights by approximately 0.2 15 8. For each experiment, calculate the Ampere force equal to the gravity of the weights F = mg. 9. Plot F versus current I in the conductor, plotting the values ​​along the I abscissa axis. This dependence was obtained at a certain constant value of the electromagnet current I EM, therefore, the magnitude of the magnetic induction is also constant. Therefore, the result obtained allows us to conclude that Ampere's law is feasible in terms of the proportionality of the Ampère force to the current strength in the conductor: F ~ I . Determination of the dependence of the magnetic induction on the current of the electromagnet 10. Place a load of a given mass on the balance pan (for example, m = 1 g). With five different values ​​of the electromagnet current I EM (for example, from 0.2 to 0.5 A), select such currents I in the frame circuit that balance the balance. Record the results in table. 3. Table 3 No. of measurement m, g I EM, A I, A B, T 1 2 3 4 5 11. Using formula (5), calculate the values ​​of magnetic induction B in each experiment. The values ​​of l and N are indicated on the installation. Plot the dependence of V on the electromagnet current, plotting the values ​​of I EM along the x-axis. 12. For one of the experiments, determine the error Δ B. Calculate the relative partial errors using the formulas Δl ΔI εl = ; ε I = ; ε m = 10 −3 . l I Record the obtained confidence interval in the report. Discuss in the conclusions: – what did the test of Ampère's law show, whether it is fulfilled; on what basis the conclusion is made; - how does the magnetic induction of an electromagnet depend on the current in its winding; - whether such a dependence will be preserved with a further increase in I EM (take into account that the magnetic field is due to the magnetization of the iron core). 16 CONTROL QUESTIONS 1. What is Ampère's law? What is the direction of Ampere's force? How does it depend on the location of the conductor in a magnetic field? 2. How is a uniform magnetic field created in work? What is the direction of the magnetic induction vector? 3. Why should a direct current flow in the frame in this work? What will the use of alternating current lead to? 4. Why is a frame consisting of several dozen turns used in the work? 5. Why is it necessary to choose a certain direction of current in the loop for the normal operation of the installation? What will change the direction of the current? How can you change the direction of the current in the loop? 6. What will change the direction of the current in the electromagnet winding? 7. Under what condition is the balance of weights achieved in work? 8. Which corollary of Ampère's law is tested in this work? References 1. Trofimova T.I. Physics course. 2000. §§ 109, 111, 112. 17 Laboratory work No. 5.3 (27) DETERMINATION OF THE SPECIFIC CHARGE OF AN ELECTRON WITH THE HELP OF A CATHONY-BEAM TUBE Purpose of the work: study of the laws governing the motion of charged particles in electric and magnetic fields; determination of the speed and specific charge of an electron. THEORETICAL MINIMUM Lorentz force A charge q moving at a speed v in an electromagnetic field is affected by the Lorentz force F l = qE + q v B , (1) where E is the electric field strength; B - magnetic field induction. The Lorentz force can be represented as the sum of the electrical and magnetic components: F l \u003d Fe + F m. The electrical component of the Lorentz force F e \u003d qE (2) does not depend on the speed of the charge. The direction of the electric component is determined by the sign of the charge: for q > 0, the vectors E and Fe are directed in the same way; at q< 0 – противоположно. Магнитная составляющая силы Лоренца Fм = q v B (3) зависит от скорости движения заряда. Модуль магнитной составляющей определяется по формуле (4) F м = qvB sin α , где α - угол между векторами v и B . Направление магнитной составляющей определяется правилом векторного произведения и знаком заряда: для положительного заряда (q >0) the right triplet of vectors is formed by the vectors v , B and Fm (Fig. 1), for a negative charge (q< 0) – векторы v , B и − F м. Направление магнитной составляющей силы Лоренца можно определить и с помощью правила левой руки. Правило левой руки: расположите ладонь левой руки так, чтобы в нее входил вектор B , а четыре пальца направьте вдоль вектора v , тогда отогнутый на 90° большой палец покажет направление силы Fм, действующей на положительный заряд. В случае отрицательного заряда направление вектора Fм противоположно. В любом случае вектор Fм перпендикулярен плоскости, в которой лежат векторы v и B . Движение заряженных частиц в магнитном поле Если частица движется вдоль линии магнитной индукции (α = 0 или α = π), то sin α = 0 . Тогда согласно выражению (4) F м = 0 . В этом случае магнитное поле не влияет на движение заряженной частицы (рис. 2). Если заряженная частица движется перпендикулярно линиям магнитной индукции (α = π 2) , то sin α = 1 . Тогда согласно (4) Fм = qvB . Так как вектор этой силы всегда перпендикулярен вектору скорости v частицы, то сила Fм создает только нормальное (центростремительное) ускорение v2 an = , при этом скорость заряженной частицы изменяется только по наr правлению, не изменяясь по модулю. Частица в этом случае равномерно движется по дуге окружности, плоскость которой перпендикулярна линиям индукции (рис. 3). Если вектор скорости v заряженной частицы составляет с вектором B угол α , то магнитная составляющая силы Лоренца будет определяться согласно (3), а модуль согласно выражению (4). В этом случае частица участвует одновременно в двух движениях: поступательном с постоянной скоростью v || и равномерном вращении по окружности со скоростью v ⊥ . В результате траектория заряженной частицы имеет форму винтовой линии (рис. 4). 19 Удельный заряд частицы Удельный заряд частицы – это отношение заряда q частицы к ее массе q m. Величина – важная характеристика заряженной частицы. Для электрона m q e Кл = = 1,78 ⋅ 1011 . m me кг МЕТОДИКА ЭКСПЕРИМЕНТА В работе изучается движение электронов в однородных электрическом и магнитном полях. Источником электронов является электронная пушка 1 электроннолучевой трубки осциллографа (рис. 5). Электрическое поле создается между парой вертикально отклоняющих пластин 2 электроннолучевой трубки при подаче на них напряжения U. (Горизонтально отклоняющие пластины 3 в работе не используются.) Напряженность E электрического поля направлена вертикально. Магнитное поле создается двумя катушками 4, симметрично расположенными вне электроннолучевой трубки, при пропускании по ним электрического тока. Вектор магнитной индукции B направлен горизонтально и перпендикулярно оси трубки. В отсутствии электрического и магнитного полей электроны движутся вдоль оси трубки с начальной скоростью v o , при этом светящееся пятно на- 20 ходится в центре экрана. При подаче напряжения U на пластины 2 между ними создается электрическое поле, напряженность которого E перпендикулярно вектору начальной скорости электронов. В результате пятно смещается. Величину y этого смещения можно измерить, воспользовавшись шкалой на экране осциллографа. Однако в электрическом поле на электрон действует согласно (2) электрическая составляющая силы Лоренца FЭ = eE , (5) где е – заряд электрона. Заряд электрона отрицательный (е < 0), поэтому сила FЭ направлена противоположно полю. Эта сила сообщает электрону ускорение a y в направлении оси Y, не влияя на величину скорости электрона вдоль оси X: v x = v 0 . Из основного закона динамики поступательного движения eE FЭ = ma y и (5) a y = , где m – масса электрона. В результате, пролетая m l область электрического поля за время t = 1 , где l1 – длина пластин, электрон vo смещается по оси Y на расстояние a y t 2 eE l12 y1 = = . 2 2mvo2 После вылета из поля электрон летит прямолинейно под некоторым v y a y t eE l1 = = . углом α к оси Х, причем согласно рисунку tgα = v x v o mvo2 21 Окончательно смещение пятна от центра экрана (рис. 2) в электрическом поле равно y = y1 + y 2 , где eE l 1 ⎛ l 1 ⎞ ⎜⎜ + l 2 ⎟⎟ . (6) y = y1 + l 2tgα = mvo2 ⎝ 2 ⎠ Если по катушкам 4 (рис. 5) пропустить электрический ток, то на пути электронов возникнет магнитное поле. Изменяя силу тока I в катушках, можно подобрать такую величину и направление магнитной индукции B , что магнитная составляющая силы Лоренца FМ скомпенсирует электрическую составляющую FЭ. В этом случае пятно снова окажется в центре экрана. Это будет при условии равенства нулю силы Лоренца eE + e v o B = 0 или E + v o B = 0 . Как видно из рис. 7, это условие выполняется, если вектор магнитной индукции B перпендикулярен векторам E и v o , что реализовано в установке. Из этого условия можно определить скорость электронов E (7) vo = . B Поскольку практически измеряется напряжение U, приложенное к пластинам, и расстояние d между ними, то пренебрегая краевыми эффектами можно считать, что E = [ U d ] , тогда U . (8) Bd Измеряя смещение у электронного пучка, вызванное электрическим полем Е, а затем подбирая такое магнитное поле В, чтобы смещение стало равным нулю, можно из уравнений (6) и (8) определить удельный заряд электрона yU e . (9) = m ⎛ l1 ⎞ 2 B dl 1 ⎜ + l 2 ⎟ ⎝2 ⎠ Схема установки показана на рис. 8. Электроннолучевая трубка расположена в корпусе осциллографа 1, на передней панели которого находится экран трубки 2 и две пары клемм. Клеммы ПЛАСТИНЫ соединены с вертикально отклоняющими пластинами трубки. Клеммы КАТУШКИ соединены с катушками 4 электромагнита, создающего магнитное поле. (Расположение катушек видно через прозрачную боковую стенку осциллографа.) Выпрямитель 5 и блок 6 служат для создания, регулировки и измерения постоянного напряжения на управляющих пластинах трубки и постоянного тока через катушки электромагнита. Переключатель K1 позволяет изменить полярность vo = 22 напряжения на пластинах, а переключатель K 2 – направление тока через катушки электромагнита. Параметры установки: d = 7,0 мм; l1 = 25,0 мм; l 2 = 250 мм. Приборы и принадлежности: осциллограф с электроннолучевой трубкой; выпрямитель; блок коммутации с электроизмерительными приборами. ПОРЯДОК ВЫПОЛНЕНИЯ РАБОТЫ 1. Заполните табл. 1 характеристик электроизмерительных приборов. Таблица 1 Наименование прибора Вольтметр Миллиамперметр Система прибора Предел измерения Цена Класс Приборная деления точности погрешность ΔU пр ΔI пр 2. Тумблером 3 (рис. 8) включите осциллограф. Ручками ЯРКОСТЬ и ФОКУС, расположенными на верхней панели осциллографа, добейтесь четкости пятна на экране. Ручкой ↔ установите пятно в центр экрана. 3. Тумблером К включите выпрямитель. Ручками П 1 и П 2 установите нулевые показания вольтметра и миллиамперметра. 4. Условия проведения эксперимента (значения напряжения U на пластинах) задаются преподавателем или вариант индивидуального занятия. 23 5. Ручкой П 1 установите нужное напряжение на пластинах и измерьте смещение у луча от центра экрана. Результат измерения в зависимости от направления смещения («вверх» или «вниз») запишите в табл.2. Таблица 2 U, В y y вверх, вниз, мм мм у, мм I1, А I2, А I , А В, Тл vo , м/с e/m, Кл/кг 6. С помощью ручки П 2 и переключателя K 2 подберите такой ток I1 в катушках, чтобы пятно вернулось в центр экрана. Значение силы тока запишите в табл. 2. 7. Измерения, указанные в пункте 5 и 6, проведите при двух других значениях напряжения U . 8. Тумблером K 1 измените полярность напряжения на пластинах и повторите измерения, указанные в пунктах 5, 6 и 7. 9. По приложенному к установке градуировочному графику электромагнита и по среднему значению силы тока I в каждом испытании определите значения магнитной индукции В и занесите их в табл. 2. 10. По формуле (8) рассчитайте скорость электронов в каждом опыте и среднее значение v o по всем испытаниям. 11. Используя формулу eU a = m vo 2 2 , рассчитайте анодное напряжение в электронной пушке. 12. По формуле (9) рассчитайте значение удельного заряда электрона в e по всем испытаниям. каждом опыте и среднее значение m 13. По результатам одного из опытов рассчитайте абсолютную погрешность удельного заряда электрона Δ me = ε e me . Здесь ε = ε y2 + εU2 + ε B2 + ε d2 + ε l21 + ε l22 . Относительные частные погрешности рассчитайте по формулам Δy ΔU 2ΔB Δd Δ l (l +l) Δl εy = ; εU = ; εB = ; εd = ; ε l1 = 1l 1 2 ; ε l 2 = l 2 . ⎞ ⎛ 1 +l y U B d l1 ⎜ 1 +l 2 ⎟ 2 ⎝2 ⎠ 2 В качестве Δу используйте приборную погрешность шкалы на экране осциллографа, в качестве ΔU – приборную погрешность вольтметра. Погрешность ΔВ определяется по градуировочному графику по величине ΔI пр. Запишите в отчет полученный доверительный интервал величины e m . 24 15. В выводах – укажите, что наблюдалось в работе; e ; согласие считается хоро– сравнить полученное и табличное значения m шим, если табличное значение попадает в найденный доверительный интервал; – указать, измерение какой величины внесло основной вклад в погрешe . ность величины m КОНТРОЛЬНЫЕ ВОПРОСЫ 1. Сила Лоренца. Направление ее составляющих. 2. Зависит ли от знака заряда сила, действующая на него со стороны: а) электрического поля; б) магнитного поля? 3. Зависит ли от скорости и направления движения заряда сила, действующая на него: а) в электрическом поле; б) в магнитном поле? 4. Как движется электрон: а) в поле между пластинами; б) слева от пластин; в) справа от пластин? 5. Отличается ли скорость электрона до и после пластин? 6. Как изменится смещение пятна на экране, если а) скорость электронов увеличить вдвое; б) анодное напряжение увеличить вдвое? 7. Изменяется ли при движении заряда в однородном магнитном поле: а) направление скорости; б) величина скорости? 8. Каким должно быть взаимное расположение однородных электрического и магнитного полей, чтобы электрон мог двигаться в них с постоянной скоростью? При каком условии возможно такое движение? 9. Какую роль в электронной пушке играют катод, модулятор, аноды? 10. Какую роль в электроннолучевой трубке играют: а) электронная пушка; б) отклоняющие пластины; в) экран? 11. Как в установке создаются однородные поля: а) электрическое; б) магнитное? 12. Как изменяется смешение пятна на экране при изменении направления тока в катушках? Библиографический список 1. Трофимова Т.И. Курс физики. 2000. §§ 114, 115. 25 Лабораторная работа № 4 (28) ОПРЕДЕЛЕНИЕ УДЕЛЬНОГО ЗАРЯДА ЭЛЕКТРОНА С ПОМОЩЬЮ ИНДИКАТОРНОЙ ЛАМПЫ Цель работы: изучение закономерностей движения заряженных частиц в электрическом и магнитном полях; определение удельного заряда электрона. ТЕОРЕТИЧЕСКИЙ МИНИМУМ Магнитная индукция (смотрите с. 4) Сила Лоренца (смотрите с. 17) Движение заряженных частиц в магнитном поле (смотрите с. 18) Удельный заряд электрона (смотрите с. 19) МЕТОДИКА ЭКСПЕРИМЕНТА В работе удельный заряд me электрона определяется путем наблюдения движения электронов в скрещенных электрическом и магнитном полях. Электрическое поле создается в пространстве между анодом и катодом вакуумной электронной лампы. Катод К расположен по оси цилиндрического анода А (рис.1), между ними приложено анодное напряжение U a . На рис. 2 показано сечение лампы плоскостью XOY . Как видим, напряженность электричеr ского поля E имеет радиальное направление. Лампа расположена в центре соленоида (катушки), создающего однородное магнитное поле, вектор индукции r B которого параллелен оси лампы. На электроны, выходящие из катода благодаря термоэлектронной эмиссии, со стороны электрического поля действует электрическая составляющая r r силы Лоренца FЭ = eE , которая ускоряет электроны к аноду. Со стороны магr r r нитного поля действует магнитная составляющая силы Лоренца FM = e , r которая направлена перпендикулярно скорости v электрона (рис. 2), поэтому его траектория искривляется. 26 На рис. 3 показаны траектории электронов в лампе при различных значениях индукции В магнитного поля. В отсутствии магнитного поля (В = 0) траектория электрона прямолинейна и направлена вдоль радиуса. При слабом поле траектория несколько искривляется. При некотором значении индукции B = B 0 траектория искривляется настолько, что касается анода. При достаточно сильном поле (B > B 0), the electron does not hit the anode at all and returns to the cathode. In the case of B = B 0, we can assume that the electron moves along a circle with a radius r = ra / 2, where ra is the radius of the anode. The force FM = evB creates a normal (centripetal) acceleration, therefore, according to the basic law of the dynamics of translational motion, mv 2 (1) = evB . r The speed of the electron can be found from the condition that the kinetic energy of the electron is equal to the work of the electric field forces on the path of the electron from the cathode to the anode mv 2 = eU a , whence 2 v= 2eU a . m (2) 27 Substituting this value for the velocity v into equation (1) and taking into account that r = ra / 2 , we obtain an expression for the specific charge of an electron 8U e = 2 a2 . m B o ra Formula (3) allows us to calculate the value (3) e m if, at a given value of the anode voltage U a, we find such a value of the magnetic induction Bo at which the electron trajectory touches the anode surface. An indicator lamp is used to observe the electron trajectory (Fig. 4). The cathode K is located along the axis of the cylindrical anode A. The cathode is heated by a filament. Between the cathode and the anode there is a screen E, which has the shape of a conical surface. The screen is covered with a layer of phosphor, which glows when electrons hit it. Parallel to the axis of the lamp, near the cathode, there is a thin wire - the antennae Y, connected to the anode. Electrons passing near the whisker are captured by it, so a shadow is formed on the screen (Fig. 5). The boundary of the shadow corresponds to the trajectory of the electrons in the lamp. The lamp is placed in the center of the solenoid, which creates a magnetic field, the induction vector r B of which is directed along the axis of the lamp. Solenoid 1 and lamp 2 are mounted on a stand (Fig. 6). The terminals located on the panel are connected to the solenoid winding, to the cathode filament, to the cathode and anode of the lamp. The solenoid is powered by rectifier 3. The source of the anode voltage and the cathode heating voltage is rectifier 4. The current in the solenoid is measured using an ammeter A, the anode voltage U a is measured by a voltmeter V. The switch P allows you to change the direction of the current in the solenoid winding. 28 Magnetic induction in the center of the solenoid, and therefore, inside the indicator lamp is determined by the relation μo I N , (4) B= 2 2 4R + l where μ0 = 1.26 10 – 6 H/m is the magnetic constant; I - current strength in the solenoid; N is the number of turns, R is the radius, l is the length of the solenoid. Substituting this value B into expression (3), we obtain a formula for determining the specific charge of an electron e 8U a (4R 2 + l 2), = m μo2 I o2 N 2ra2 (5) where I o is the value of the current in the solenoid, at which the electron trajectory touches the outer edge of the screen. Taking into account that Ua and I0 are practically measured, and the values ​​N, R, l, ra are the installation parameters, from formula (5) we obtain a calculation formula for determining the specific charge of an electron U e (6) = A ⋅ 2a , m Io where A - installation constant A= (8 4R 2 + l 2 μo2 N 2ra2). (7) 29 Instruments and accessories: laboratory stand with indicator lamp, solenoid, ammeter and voltmeter; two rectifiers. ORDER OF PERFORMANCE OF WORK 1. Fill in tab. 1 characteristics of the ammeter and voltmeter. Table 1 Name Device instrument system Voltmeter Measurement limit Division value Accuracy class ΔI pr Ammeter 2. 3. 4. Instrument error ΔU pr Check the correct connection of the wires according to fig. 6. Move the adjusting knobs of the rectifiers to the extreme left position. Write down in the report the parameters indicated on the installation: the number of turns N, the length l and the radius R of the solenoid. Anode radius ra = 1.2 cm. Record in the table. 2 the results of measurements of the value of U a given by the teacher or a variant of an individual task. Table 2 No. of measurements Ua , V I o1 , А I o2 , А Io , А em , C/kg 1 2 3 5. rectifier adjusting knob 4 required voltage value U a . At the same time, the lamp screen starts to glow. Gradually increase the current I in the solenoid using the rectifier adjustment knob 3 and observe the curvature of the electron trajectory. Select and write in the table. 2 is the value of the current I o1 at which the electron trajectory touches the outer edge of the screen. 30 7. 8. 9. Reduce solenoid current to zero. Move the switch P to another position, thereby changing the direction of the current in the solenoid to the opposite. Select and write in the table. 2 is the value of the current I o 2 at which the electron trajectory again touches the outer edge of the screen. The measurements indicated in paragraphs 5-7, carry out at two more values ​​​​of the anode voltage U a. For each value of the anode voltage, calculate and record in the table. 2 average current values ​​I o = (I o1 + I o 2) / 2. 10. According to the formula (7), calculate the constant A of the installation and write down the result in the report. 11. Using the value of A and the average value of I o , calculate according to the formula (6) e for each value of U a . Calculation results for write in table. 2. i. + ε 2ra + ε l2 + ε 2R , ΔU a 2ΔI o 2Δra 2lΔl 8RΔR , ε ra = , ε Io = , εl = , . ε = R Io Ua ra 4R 2 + l 2 4R 2 + l 2 Here ΔU a is the instrumental error of the voltmeter. As the error of the current strength ΔI o, choose the largest of the two errors: random in εU a \u003d error ΔI 0sl \u003d I o1 - I o 2 2 and the instrumental error of the ammeter ΔI pr (see table of instrument characteristics). Errors Δra , Δl , ΔR are defined as the errors of values ​​given numerically. 14. The final result of determining the specific charge of an electron is written as a confidence interval: = ±Δ. m m m 31 15. In the conclusions on the work, write down: - what was studied in the work; - how does the radius of curvature of the electron trajectory depend (qualitatively) on the magnitude of the magnetic field; - how and why the direction of the current in the solenoid affects the electron trajectory; - what result is obtained; - whether the table value of the specific charge of an electron falls within the obtained confidence interval; - the measurement error of what value has made the main contribution to the measurement error of the specific charge of the electron. CONTROL QUESTIONS What determines and how they are directed: a) the electric component of the Lorentz force; b) the magnetic component of the Lorentz force? 2. How are they directed and how do they change in magnitude in an indicator lamp: a) electric field; b) magnetic field? 3. How does the velocity of electrons in the lamp change in magnitude with the distance from the cathode? Does a magnetic field affect the speed? 4. What is the trajectory of electrons in a lamp with magnetic induction: a) B = 0; b) B = Bo; c) B< Bo ; г) B >Bo? 5. What is the acceleration of electrons near the anode equal to and how is it directed at magnetic induction B = Bo ? 6. What role do they play in the indicator lamp: a) screen; b) a wire-whisker? 7. Why does the brightness of the lamp screen increase with an increase in the anode voltage U a? 8. How is created in the lamp: a) electric field; b) magnetic field? 9. What role does the solenoid play in this work? Why should the solenoid have a sufficiently large number of turns (several hundred)? 10. Does the work: a) electrical; b) the magnetic component of the Lorentz force? 1. Bibliographic list 1. Trofimova T.I. Course of Physics, 2000, § 114, 115. 32 Laboratory work No. 5.5 (29) INVESTIGATION OF THE MAGNETIC PROPERTIES OF A FERROMAGNET The purpose of the work: the study of the magnetic properties of matter; determination of the magnetic hysteresis loop of a ferromagnet. THEORETICAL MINIMUM Magnetic properties of a substance All substances, when introduced into a magnetic field, exhibit magnetic properties to some extent, and according to these properties they are divided into diamagnets, paramagnets, and ferromagnets. The magnetic properties of matter are due to the magnetic moments of atoms. Any substance placed in an external magnetic field creates its own magnetic field, which is superimposed on the external field. The quantitative characteristic of such a state of matter is the magnetization J, equal to the sum of the magnetic moments of atoms in a unit volume of the substance. The magnetization is proportional to the intensity H of the external magnetic field J = χH , (1) where χ is a dimensionless quantity, which is called the magnetic susceptibility. The magnetic properties of matter, in addition to the value of χ, are also characterized by magnetic permeability μ = χ +1. (2) The magnetic permeability μ is included in the relation that relates the strength H and the induction B of the magnetic field in the substance B = μo μ H , (3) where μo = 1.26 ⋅10 −6 H/m is the magnetic constant. The magnetic moment of diamagnetic atoms in the absence of an external magnetic field is zero. In an external magnetic field, the induced magnetic moments of atoms, according to the Lenz rule, are directed against the external field. The magnetization J is directed in the same way, therefore, for diamagnets χ< 0 и μ < 1 . После удаления диамагнетика из поля его намагниченность вследствие теплового движения атомов исчезает. Магнитные моменты атомов парамагнетиков в отсутствии внешнего магнитного поля не равны нулю, но без внешнего поля они ориентированы хаотично. Внешнее магнитное поле приводит к частичной ориентации магнитных моментов по направлению внешнего поля в той степени, насколько это позволяет тепловое движение атомов. Для парамагнетиков 0 < χ << 1 ; величина μ чуть превосходит единицу. При выключении внешнего магнитного поля намагниченность парамагнетиков исчезает под действием теплового движения. Магнитные моменты атомов ферромагнетиков в пределах малых областей (доменов) самопроизвольно (спонтанно) ориентированы одинаково. В 33 отсутствии внешнего магнитного поля в размагниченном ферромагнетике магнитные моменты доменов ориентированы хаотично. При включении внешнего магнитного поля результирующие магнитные моменты доменов ориентируются по полю, значительно усиливая его. Магнитная восприимчивость χ ферромагнетиков может достигать нескольких тысяч. Магнитный гистерезис Величина намагниченности J ферромагнетика зависит от напряженности Н внешнего поля и от предыстории образца. На рис. 1 приведена зависимость J(H), которая характеризует процесс намагничивания ферромагнетика. В точке 0 ферромагнетик полностью размагничен. По мере увеличения напряженности Н намагниченность J образца увеличивается нелинейно. Участок 0-1 называется основной кривой намагничивания. Уже при сравнительно небольших значениях Н намагниченность стремится к насыщению Jнас, что соответствует ориентации всех магнитных моментов доменов по направлению индукции внешнего поля. Если после достижения Jнас уменьшать напряженность внешнего магнитного поля, то намагниченность будет изменяться по кривой 1-2, расположенной выше основной кривой намагниченности. Когда внешнее поле станет равным нулю, в ферромагнетике сохранится остаточная намагниченность Jост. При противоположном направлении напряженности внешнего поля намагниченность, следуя по кривой 2-3, вначале обратится в ноль, а затем, также изменив направление на противоположное, будет стремиться к насыщению. Значение напряженности Нк, при котором J обращается в ноль, называется коэрцитивной силой. Если продолжить процесс перемагничивания вещества, то получится замкнутая кривая 1-2-3-4-1, которая называется петлей магнитного гистерезиса. По форме петли гистерезиса ферромагнетики разделяются на жесткие и мягкие. Жестким ферромагнетикам соответствует широкая петля и большая коэрцитивная сила (Н К ≥ 10 3 А/м). Такие вещества используются для изготовления постоянных магнитов. Мягким ферромагнетикам присуща узкая петля и небольшое значение коэрцитивной силы (Н К = 1K10 2 А/м). Они используются для изготовления сердечников трансформаторов, электромагнитов, реле. Ферромагнетики в отличие от диамагнетиков и парамагнетиков обладают существенной особенностью: для каждого из таких материалов имеется присущая только им температура, при которой исчезают ферромагнитные свойства. Эта температура называется точкой Кюри. При нагревании материала выше точки Кюри ферромагнетик превращается в парамагнетик. Это 34 объясняется тем, что при высоких температурах доменные образования в ферромагнетике исчезают. МЕТОДИКА ЭКСПЕРИМЕНТА Намагниченность ферромагнитного образца в данной работе измеряется с помощью магнитометрической установки, схема которой показана на рис. 2. Между одинаковыми соленоидами (катушками) 1 на их оси расположен компас 2. По соленоидам протекают одинаковые токи силой I , но в про- тивоположных направлениях. Поэтому вблизи магнитной стрелки компаса соленоиды создают равные, но противоположные по направлению магнитные поля, которые взаимно компенсируются и не вызывают отклонения стрелки. В этом случае стрелка устанавливается в направлении горизонтальной составляющей B Г индукции магнитного поля Земли. Ось соленоидов предварительно ориентируется перпендикулярно вектору B Г. При помещении в один из соленоидов ферромагнитного образца 3 образец намагничивается и создает вблизи стрелки компаса некоторое магнитное поле с индукцией B ⊥ B Г. Стрелка повернется на угол ϕ и установится вдоль результирующего поля B рез = B + B Г. Как следует из рис. 2, (1) B = B Г ⋅ tgϕ . Величина индукции В магнитного поля, создаваемого образцом вблизи стрелки, пропорциональна намагниченности J образца B = kJ , (2) где коэффициент k зависит от формы и размеров образца и его расположения относительно компаса, то есть является постоянной установки. Таким образом, расчетная формула для определения намагниченности B tgϕ . (3) J= Г k 35 Напряженность H магнитного поля соленоида может быть рассчитана по формуле H = nI , (4) где I - сила тока в соленоиде; n - число витков, приходящихся на единицу длины соленоида. Значения k и n указаны на установке. Общий вид установки показан на рис.3. Соленоиды 1, компас 2 и амперметр 3 размещены на подставке 4. С помощью переключателя 5 изменяется направление тока в соленоидах. Соленоиды питаются от выпрямителя 6. Переключателем 9 соленоиды подключаются к постоянному или к переменному напряжению. Приборы и принадлежности: магнитометрическая установка; выпрямитель; ферромагнитный образец. ПОРЯДОК ВЫПОЛНЕНИЯ РАБОТЫ Объем работы, и условия проведения опыта устанавливаются преподавателем или вариантом индивидуального задания. 1. Заполните табл. 1 характеристик миллиамперметра. Таблица 1 Наименование прибора Миллиамперметр Система прибора Предел измерения Цена Класс Приборная деления точности погрешность ΔI пр 2. Расположите подставку с соленоидами так, чтобы ось соленоидов была перпендикулярна горизонтальной составляющей B Г магнитного поля Земли. Компас закреплен так, что при этом его стрелка установится на нуле- 36 вое деление. Подайте на соленоиды постоянное напряжение, для этого переключатель 9 (рис.3) поставьте в положение (=). При этом соленоиды подключаются к клеммам 7. Не вставляя ферромагнитный образец в соленоид, включите выпрямитель и убедитесь, что магнитные поля соленоидов вблизи стрелки компаса компенсируются: стрелка не должна заметно отклоняться при увеличении силы тока в соленоидах с помощью ручки 10 выпрямителя. 3. Выключите выпрямитель, вставьте образец в один из соленоидов. Далее необходимо размагнитить образец. Для этого подключите соленоиды к клеммам 8 переменного напряжения, то есть, поставьте переключатель 9 в положение (~) . Включите выпрямитель и ручкой 10 доведите силу переменного тока в соленоидах до 2 А (измеряется амперметром выпрямителя) и постепенно уменьшайте его до нуля. Магнитная стрела должна находиться попрежнему на нулевом делении. 4. При нулевом значении силы тока в соленоидах (ручка 10 находится в крайнем левом положении) поставьте переключатель 9 в положение (=), подключив тем самым соленоиды к источнику постоянного напряжения. Установка и образец готовы к проведению изучения магнитных свойств образца. 5. Ступенчато увеличивая силу тока I от 0 до 500 мА, измерьте угол ϕ отклонения стрелки компаса, соответствующий каждому значению силы тока I . В интервале значений от 0 до 100 мА измерения надо делать через каждые 20 мА, а при больших значениях – через каждые 100 мА. Силу тока можно изменять только в сторону возрастания, уменьшение силы тока при его регулировке недопустимо. Измеренные значения I и ϕ запишите в две первые колонки (Ток +) табл. 2. Таблица 2 Ток + I , мА ϕ , град. Ток – I , мА ϕ , град. Ток + I , мА ϕ , град. (Еще 17 строк) В результате выполнения этого пункта строится основная кривая намагничивания (участок 0–1 на рис. 1). 6. Уменьшая ток в соленоидах до нуля так же, как указано в пункте 4, измерьте необходимые величины на участке 1–2 петли гистерезиса (рис.1). При этом ток можно регулировать только в сторону уменьшения. Результаты измерений I и ϕ запишите по-прежнему в две первые колонки табл. 2. 7. При нулевом значении силы тока в соленоидах переключите тумблер 5 (рис.3) в другое крайнее положение, изменив при этом направление тока в соленоидах на противоположное. Измерьте необходимые величины на участке 2–3 кривой гистерезиса (рис. 1). При этом силу тока следует регулировать только в направлении увеличения такими же ступенями, как в пункте 4. Результаты измерений I и ϕ запишите в две средние колонки «Ток–». Обратите внимание, что на этом участке кривой намагничивания происходит изме- 37 нение знака величины J и, следовательно, знака угла ϕ . Это надо отметить в таблице, указывая знак ϕ . 8. Постепенно уменьшая ток до нуля, измерьте величины I и ϕ на участке 3–4 кривой намагничивания. Результаты запишите в колонки «Ток–». 9. Тумблером 5 (рис. 3) измените, направление тока и, увеличивая силу тока, измерьте необходимые величины на последнем участке 4–1 кривой гистерезиса. Результаты измерений I и ϕ запишите в две правые колонки (Ток +) с указанием знака угла ϕ . 10. Постройте кривую магнитного гистерезиса, откладывая по осям координат (в зависимости от задания) или I и ϕ , или J и H , или B и H . 11. На основании полученной кривой гистерезиса рассчитайте по формулам (3) и (4) остаточную намагниченность J ост образца и коэрцитивную силу Н к. Величины k и n указаны на установке. 12. Для одной из точек на основной кривой намагничивания рассчитайте по формулам (3), (4), (1) и (2) значения магнитной восприимчивости χ и магнитной проницаемости μ ферромагнетика. КОНТРОЛЬНЫЕ ВОПРОСЫ 1. Чем обусловлены магнитные свойства: а) парамагнетиков; б) ферромагнетиков; в) диамагнетиков? 2. Дайте определение намагниченности. 3. Что характеризуют: а) магнитная восприимчивость; б) магнитная проницаемость? 4. Что такое основная кривая намагничивания? 5. Что такое: а) остаточная намагниченность; б) коэрцитивная сила; в) намагниченность насыщения? 6. В чем различие между жесткими и мягкими ферромагнетиками? Где они применяются? 7. Какая температура для ферромагнетиков называется точкой Кюри? 8. Как располагается магнитная стрелка, если ток в соленоидах отсутствует? Почему включение тока в соленоидах не влияет на положение стрелки? 9. Как надо ориентировать установку перед началом измерений? 10. Как устанавливается магнитная стрелка при намагничивании образца? 11. Почему перед получением петли гистерезиса образец должен быть размагничен? Как осуществляется размагничивание? ЛИТЕРАТУРА 1. Трофимова Т.И. Курс физики. 2000. § 132, 133, 135, 136. 2. Матвеев Н.Н., Постников В.В., Саушкин В.В. Физика. 2002.- С. 79-82. 38 ПРИЛОЖЕНИЕ 1. НЕКОТОРЫЕ ФИЗИЧЕСКИЕ ПОСТОЯННЫЕ Универсальная газовая постоянная Магнитная постоянная Электрическая постоянная Заряд электрона Масса электрона Удельный заряд электрона Горизонтальная составляющая индукции магнитного поля Земли (на широте Воронежа) R = 8,31 Дж/(моль⋅К) μ o = 1,26⋅10 – 6 Гн/м ε o = 8,85⋅10 – 12 Ф/м е = 1,6⋅10 – 19 Кл m = 0,91⋅10 – 30 кг e/m = 1,76⋅10 11 Кл/кг B Г = 2,0⋅10 – 5 Тл 2. ДЕСЯТИЧНЫЕ ПРИСТАВКИ К НАЗВАНИЯМ ЕДИНИЦ Г – гига (10 9) М – мега (10 6) к – кило (10 3) д – деци (10 – 1) с – санти (10 – 2) м – милли (10 – 3) Например: 1 кОм = 10 3 Ом; мк – микро (10 – 6) н – нано (10 – 9) п – пико (10 – 12) 1мА = 10 – 3 А; 1 мкФ = 10 – 6 Ф. 3. УСЛОВНЫЕ ОБОЗНАЧЕНИЯ НА ШКАЛЕ ЭЛЕКТРОИЗМЕРИТЕЛЬНЫХ ПРИБОРОВ Обозначение единицы измерения Ампер Вольт Миллиампер, милливольт Микроампер, микровольт А V mA, mV μ А, μ V Обозначение принципа действия (системы) прибора Магнитоэлектрический прибор с подвижной рамкой Электромагнитный прибор с подвижным ферромагнитным сердечником Положение шкалы прибора Горизонтальное Вертикальное Обозначение рода тока Прибор для измерения постоянного тока (напряжения) Прибор для измерения переменного тока (напряжения) Другие обозначения Класс точности Изоляция между электрической цепью прибора и корпусом испытана напряжением (кВ) ⊥ –– ~ 0,5 1,0 и др. 39 Пределом измерения прибора называется то значение измеряемой величины, при котором стрелка прибора отклоняется до конца шкалы. На многопредельных приборах пределы измерений указаны около клемм или около переключателей диапазонов. Цена деления шкалы равна значению измеряемой величины, которое вызывает отклонение стрелки прибора на одно деление шкалы. Если предел измерения xm и шкала имеет N делений, то цена деления c = x m / N . Δ x np Класс точности прибора γ = ⋅ 100% , где Δ x np - максимальная xm погрешность прибора; x m - предел измерения. Значение γ приведено на шкале прибора. Зная класс точности γ , можно определить приборную погрешность x Δ x np = γ m ., 100 БИБЛИОГРАФИЧЕСКИЙ СПИСОК Основная литература 1 Трофимова, Т.И. Курс физики [Текст]: Учебное пособие.– 6-е изд. – М.: Высш. шк., 2000.– 542 с. Дополнительная литература 1 Курс физики [Текст] / под ред. В.Н. Лозовского.– 2-е изд., испр.– СПб.: Лань, 2001.–Т.1.– 576 с. 2 Курс физики [Текст] / под ред. В.Н. Лозовского.– 2-е изд., испр.– СПб.: Лань.– 2001.Т.2.– 592 с. 3 Дмитриева, В.Ф. Основы физики [Текст]: учеб. пособие / В.Ф. Дмитриева, В.Л. Прокофьев – М.: Высш. шк., 2001.– 527 с. 4 Грибов, Л.А. Основы физики [Текст] / Л.А. Грибов, Н.И. Прокофьва.– М.: Гароарика, 1998.– 456 с. 40 Учебное издание Бирюкова Ирина Петровна Бородин Василий Николаевич Камалова Нина Сергеевна Евсикова Наталья Юрьевна Матвеев Николай Николаевич Саушкин Виктор Васильевич Физика Лабораторный практикум Магнетизм ЭЛЕКТРОННАЯ ВЕРСИЯ

Ministry of Education and Science of the Russian Federation

Baltic State Technical University "Voenmeh"

ELECTROMAGNETISM

Laboratory workshop in physics

Part 2

Edited by L.I. Vasilyeva and V.A. Zhivulina

St. Petersburg

Compiled by: D.L. Fedorov, Dr. phys.-math. sciences, prof.; L.I. Vasiliev, prof.; ON THE. Ivanova, Assoc.; E.P. Denisov, Assoc.; V.A. Zhivulin, Assoc.; A.N. Starukhin, prof.

UDC 537.8(076)

E

Electromagnetism: laboratory workshop in physics / comp.: D.L. Fedorov [and others]; Balt. state tech. un-t. - St. Petersburg, 2009. - 90 p.

The workshop contains a description of laboratory works Nos. 14-22 on the topics "Electricity and Magnetism" in addition to the description of works Nos. 1-13 presented in the workshop of the same name, published in 2006.

Designed for students of all specialties.

45

UDC 537.8(076)

Reviewer: Dr. Tech. sciences, prof., head. cafe Information and Energy Technologies BSTU S.P. Prisyazhnyuk

Approved

editorial and publishing

© BSTU, 2009

Laboratory work No. 14 Studying the electrical properties of ferroelectrics

Objective – to study the polarization of ferroelectrics depending on the strength of the electric field E, get curve E=f(E), study dielectric hysteresis, determine dielectric losses in ferroelectrics.

Brief information from the theory

As is known, dielectric molecules are equivalent in their electrical properties to electric dipoles and can have an electric moment

where q is the absolute value of the total charge of the same sign in the molecule (i.e., the charge of all nuclei or all electrons); l is a vector drawn from the "center of gravity" of the negative charges of electrons to the "center of gravity" of the positive charges of the nuclei (dipole arm).

The polarization of dielectrics is usually described in terms of rigid and induced dipoles. An external electric field either orders the orientation of hard dipoles (orientational polarization in dielectrics with polar molecules) or leads to the appearance of completely ordered induced dipoles (polarization of electron and ion displacements in dielectrics with nonpolar molecules). In all these cases, the dielectrics are polarized.

The polarization of a dielectric lies in the fact that, under the action of an external electric field, the total electric moment of the molecules of the dielectric becomes nonzero.

The quantitative characteristic of the polarization of a dielectric is the polarization vector (or polarization vector), which is equal to the electric moment per unit volume of the dielectric:

, (14.2)

is the vector sum of electric dipole moments of all dielectric molecules in a physically infinitesimal volume
.

For isotropic dielectrics, the polarization related to the strength of the electric field at the same point by the ratio

æ
, (14.3)

where æ is a coefficient that, in the first approximation, does not depend on and called the dielectric susceptibility of matter; =
F/m is the electrical constant.

To describe the electric field in dielectrics, in addition to the intensity and polarization , use the electric displacement vector , defined by the equality

. (14.4)

Taking into account (14.3), the displacement vector can be represented as

, (14.5)

where
æ is a dimensionless quantity called the permittivity of the medium. For all dielectrics, æ > 0 and ε > 1.

Ferroelectrics are a special group of crystalline dielectrics that, in the absence of an external electric field, have spontaneous (spontaneous) polarization in a certain range of temperatures and pressures, the direction of which can be changed by an electric field and, in some cases, by mechanical stresses.

Unlike conventional dielectrics, ferroelectrics have a number of characteristic properties that were studied by Soviet physicists I.V. Kurchatov and P.P. Kobeko. Let us consider the main properties of ferroelectrics.

Ferroelectrics are characterized by very high dielectric constants , which can reach values ​​of the order
. For example, the dielectric constant of Rochelle salt NaKC 4 H 4 O 6 ∙4H 2 O at room temperature (~20°C) is close to 10000.

A feature of ferroelectrics is the nonlinear nature of the polarization dependence R, and hence the electric displacement D from field strength E(Fig. 14.1). In this case, the permittivity of ferroelectrics ε turns out to depend on E. On fig. 14.2 shows this dependence for Rochelle salt at a temperature of 20°C.

All ferroelectrics are characterized by the phenomenon of dielectric hysteresis, which consists in a delay in the change in polarization R(or displacement D) when changing the field strength E. This delay is due to the fact that R(or D) is not only determined by the value of the field E, but also depends on the previous state of polarization of the sample. With cyclic changes in field strength E addiction R and offsets D from E expressed by a curve called a hysteresis loop.

On fig. 14.3 shows the hysteresis loop in coordinates D, E.

With increasing field E bias D in a sample that was not initially polarized changes along the curve OAB. This curve is called the initial or main polarization curve.

As the field decreases, the ferroelectric initially behaves like a conventional dielectric (in the section VA there is no hysteresis), and then (from the point BUT) the change in displacement lags behind the change in tension. When the field strength E= 0, the ferroelectric remains polarized and the magnitude of the electric displacement equal to
, is called residual displacement.

To remove the residual displacement, it is necessary to apply an electric field of the opposite direction to the ferroelectric with a strength of - . the value called the coercive field.

If the maximum value of the field strength is such that the spontaneous polarization reaches saturation, then a hysteresis loop is obtained, called the limit cycle loop (solid curve in Fig. 14.3).

If, however, saturation is not reached at the maximum field strength, then a so-called partial cycle loop is obtained, lying inside the limit cycle (dashed curve in Fig. 14.3). There can be an infinite number of private cycles of repolarization, but at the same time, the maximum values ​​of the displacement D partial cycles always lie on the main polarization curve of the OA.

The ferroelectric properties strongly depend on temperature. For every ferroelectric there is a temperature , above which its ferroelectric properties disappear and it turns into an ordinary dielectric. Temperature called the Curie point. For barium titanate BaTi0 3 the Curie point is 120°C. Some ferroelectrics have two Curie points (upper and lower) and behave like ferroelectrics only in the temperature range between these points. These include Rochelle salt, for which the Curie points are +24°С and –18°С.

On fig. 14.4 shows a graph of the temperature dependence of the permittivity of a BaTi0 3 single crystal (The BaTi0 3 crystal in the ferroelectric state is anisotropic. In Fig. 14.4, the left branch of the graph refers to the direction in the crystal, perpendicular to the axis of spontaneous polarization.) In a sufficiently large temperature range, the values ВаTi0 3 significantly exceed the values ordinary dielectrics, for which
. Near the Curie point, there is a significant increase (anomaly).

All the characteristic properties of ferroelectrics are associated with the existence of spontaneous polarization in them. Spontaneous polarization is a consequence of the inherent asymmetry of the unit cell of the crystal, which leads to the appearance of a dipole electric moment in it. As a result of the interaction between the individual polarized cells, they are arranged so that their electric moments are oriented parallel to each other. The orientation of the electric moments of many cells in one direction leads to the formation of regions of spontaneous polarization, called domains. Obviously, each domain is polarized to saturation. The linear dimensions of the domains do not exceed 10 -6 m.

In the absence of an external electric field, the polarization of all domains is different in direction; therefore, the crystal as a whole turns out to be unpolarized. This is illustrated in Fig. 14.5, a, where the domains of the sample are schematically depicted, the arrows show the directions of spontaneous polarization of different domains. Under the influence of an external electric field, a reorientation of the spontaneous polarization occurs in a multidomain crystal. This process is carried out: a) by displacement of domain walls (domains whose polarization makes an acute angle with an external field, grow at the expense of domains in which
); b) rotation of electrical moments - domains - in the direction of the field; c) the formation and germination of nuclei of new domains, the electric moments of which are directed along the field.

The rearrangement of the domain structure, which occurs when an external electric field is applied and increased, leads to the appearance and growth of the total polarization R crystal (nonlinear section OA in fig. 14.1 and 14.3). In this case, the contribution to the total polarization R, in addition to the spontaneous polarization, the induced polarization of the electron and ion displacements also contributes, i.e.
.

At a certain field strength (at the point BUT) a single direction of spontaneous polarization is established in the entire crystal, coinciding with the direction of the field (Fig. 14.5, b). The crystal is said to become single-domain with the direction of spontaneous polarization parallel to the field. This state is called saturation. Field increase E upon reaching saturation, it is accompanied by a further increase in the total polarization R crystal, but now only due to induced polarization (section AB in fig. 14.1 and 14.3). At the same time, the polarization R and offset D almost linearly dependent on E. Extrapolating a Linear Plot AB on the y-axis, one can estimate the spontaneous saturation polarization
, which is approximately equal to the value
cut off by the extrapolated section on the y-axis:
. This approximate equality follows from the fact that for most ferroelectrics
and
.

As noted above, at the Curie point, when a ferroelectric is heated, its special properties disappear and it turns into an ordinary dielectric. This is explained by the fact that at the Curie temperature a ferroelectric phase transition occurs from the polar phase, characterized by the presence of spontaneous polarization, to the nonpolar phase, in which spontaneous polarization is absent. This changes the symmetry of the crystal lattice. The polar phase is often called the ferroelectric phase, while the non-polar phase is called the paraelectric phase.

In conclusion, we discuss the problem of dielectric losses in ferroelectrics due to hysteresis.

Energy losses in dielectrics in an alternating electric field, called dielectric, can be associated with the following phenomena: a) polarization time lag R from field strength E due to molecular thermal motion; b) the presence of small conduction currents; c) the phenomenon of dielectric hysteresis. In all these cases, an irreversible conversion of electrical energy into heat occurs.

Dielectric losses cause that in the section of the AC circuit containing the capacitor, the phase shift between current and voltage fluctuations is never exactly equal
, but it always turns out to be less than
, at the corner called the loss angle. Dielectric losses in capacitors are estimated by the loss tangent:

, (14.6)

where is the reactance of the capacitor; R- loss resistance in the capacitor, determined from the condition: the power released on this resistance when an alternating current passes through it is equal to the power losses in the capacitor.

The loss tangent is the reciprocal of the quality factor Q:
, and to determine it, along with (14.6), the expression can be used

, (14.7)

where
– energy losses for the oscillation period (in the circuit element or in the entire circuit); W– oscillation energy (maximum for the circuit element and total for the entire circuit).

We use formula (14.7) to estimate the energy losses caused by the dielectric hysteresis. These losses, like the hysteresis itself, are a consequence of the irreversible nature of the processes responsible for the reorientation of spontaneous polarization.

Let us rewrite (14.7) as

, (14.8)

where is the energy loss of the alternating electric field due to the dielectric hysteresis per unit volume of the ferroelectric during one period; is the maximum energy density of the electric field in the ferroelectric crystal.

Since the volumetric energy density of the electric field

(14.9)

then with an increase in the field strength by
it changes accordingly to . This energy is expended on the repolarization of a unit volume of the ferroelectric and is used to increase its internal energy, i.e. to heat it up. Obviously, for one complete period, the value of dielectric losses per unit volume of a ferroelectric is determined as

(14.10)

and is numerically equal to the area of ​​the hysteresis loop in the coordinates D, E. The maximum energy density of the electric field in the crystal is:

, (14.11)

where and
are the amplitudes of the strength and displacement of the electric field.

Substituting (14.10) and (14.11) into (14.8), we obtain the following expression for the tangent of the dielectric loss angle in ferroelectrics:

(14.12)

Ferroelectrics are used to manufacture capacitors of large capacity, but small sizes, to create various non-linear elements. Many radio engineering devices use variconds - ferroelectric capacitors with pronounced nonlinear properties: the capacitance of such capacitors strongly depends on the magnitude of the voltage applied to them. Variconds are characterized by high mechanical strength, resistance to vibration, shaking, moisture. The disadvantages of variconds are a limited range of operating frequencies and temperatures, high values ​​of dielectric losses.

9. Enter the obtained data in the upper half of table 2, presenting the results in the form.

10. Press the switch 10, which will allow you to make measurements according to the scheme of fig. 2 (accurate voltage measurement). Carry out the operations indicated in paragraphs. 3-8, replacing in paragraph 6 the calculation according to formula (9) with the calculation according to formula (10).

11. Enter the data obtained during calculations and measurements with the switch 10 pressed (see item 10) in the lower half of Table 2, presenting the measurement results in the form Mode of operation Precise measurement of currents Accurate measurement of voltage 1. What is the purpose of the work?

2. What methods of measuring active resistance are used in this work?

3. Describe the working setup and the course of the experiment.

4. Write down the working formulas and explain the physical meaning of the quantities included in them.

1. Formulate Kirchhoff's rules for calculating branched electrical circuits.

2. Derive working formulas (9) and (10).

3. At what ratios of R, RA and RV is the first measurement scheme used? Second? Explain.

4. Compare the results obtained in this work by the first and second methods. What conclusions can be drawn regarding the accuracy of measurements by these methods? Why?

5. Why in step 4 is the regulator set to such a position that the voltmeter needle deviates by at least 2/3 of the scale?

6. Formulate Ohm's law for a homogeneous section of the chain.

7. Formulate the physical meaning of resistivity. On what factors does this value depend (see work No. 32)?

8. On what factors does the resistance R of a homogeneous isotropic metallic conductor depend?

SOLENOID INDUCTANCE DETERMINATION

The purpose of the work is to determine the inductance of the solenoid by its resistance to alternating current.

Instruments and accessories: solenoid under test, sound generator, electronic oscilloscope, AC milliammeter, connecting wires.

The phenomenon of self-induction. Inductance The phenomenon of electromagnetic induction is observed in all cases when the magnetic flux penetrating the conducting circuit changes. In particular, if an electric current flows in a conducting circuit, then it creates a magnetic flux F penetrating this circuit.

When the current strength I changes in any circuit, the magnetic flux F also changes, as a result of which an electromotive force (EMF) of induction arises in the circuit, which causes an additional current (Fig. 1, where 1 is a conducting closed circuit, 2 are the lines of force of the magnetic field created loop current). This phenomenon is called self-induction, and the additional current caused by the self-induction EMF is the self-induction extra current.

The phenomenon of self-induction is observed in any closed electrical circuit in which an electric current flows, when this circuit is closed or opened.

Consider what the value of the EMF s of self-induction depends on.

The magnetic flux F, penetrating a closed conducting circuit, is proportional to the magnetic induction B of the magnetic field created by the current flowing in the circuit, and the induction B is proportional to the strength of the current.

Then the magnetic flux Ф is proportional to the current strength, i.e.

where L is the inductance of the circuit, H (Henry).

From (1) we obtain The inductance of the circuit L is a scalar physical quantity equal to the ratio of the magnetic flux Ф penetrating this circuit to the magnitude of the current flowing in the circuit.

Henry is the inductance of such a circuit in which, at a current strength of 1A, a magnetic flux of 1Wb occurs, i.e. 1 Hn = 1.

According to the law of electromagnetic induction Substituting (1) into (3), we obtain the EMF of self-induction:

Formula (4) is valid for L=const.

Experience shows that with an increase in inductance L in an electric circuit, the current in the circuit increases gradually (see Fig. 2), and with a decrease in L, the current decreases just as slowly (Fig. 3).

The strength of the current in the electrical circuit during a short circuit changes by Curves of changes in the strength of the current are shown in fig. 2 and 3.

The inductance of the circuit depends on the shape, size and deformation of the circuit, on the magnetic state of the medium in which the circuit is located, as well as on other factors.

Find the inductance of the solenoid. A solenoid is a cylindrical tube made of a non-magnetic, non-conductive material, on which a thin metal conductive wire is wound tightly, coil to coil. On fig. 4 shows a section of the solenoid along a cylindrical tube in diameter (1 - magnetic field lines).

The length l of the solenoid is much larger than the diameter d, i.e.

ld. If l d, then the solenoid can be considered as a short coil.

The diameter of the thin wire is much smaller than the diameter of the solenoid. To increase the inductance, a ferromagnetic core with magnetic permeability is placed inside the solenoid. If ld, then when current flows inside the solenoid, a uniform magnetic field is excited, the induction of which is determined by the formula where o = 4 10-7 H/m is the magnetic constant; n = N/l is the number of turns per unit length of the solenoid; N is the number of turns of the solenoid.

Outside the solenoid, the magnetic field is practically zero. Since the solenoid has N turns, the total magnetic flux (flux linkage) penetrating the cross section S of the solenoid is where Ф = BS is the flux penetrating one coil of the solenoid.

Substituting (5) into (6) and taking into account the fact that N = nl, we obtain On the other hand, Comparing (7) and (8), we obtain The cross-sectional area of ​​the solenoid is Equal to Taking into account (10), formula (9) will be written as Define the inductance of the solenoid is possible by connecting the solenoid to an AC electrical circuit with a frequency. Then the total resistance (impedance) is determined by the formula where R is the active resistance, Ohm; L = xL - inductive resistance; \u003d xs - capacitance of a capacitor with a capacitance C.

If there is no capacitor in the electrical circuit, i.e.

the capacitance of the circuit is small, then xc xL and formula (12) will look like Then Ohm's law for alternating current will be written as where Im, Um are the amplitude values ​​of the current and voltage.

Since = 2, where is the frequency of alternating current oscillations, then (14) will take the form From (15) we obtain a working formula for determining the inductance:

To perform the work, assemble the circuit according to the scheme of Fig. 5.

1. Set the oscillation frequency on the sound generator as indicated by the teacher.

2. Using an oscilloscope, measure the voltage amplitude Um and the frequency.

3. Using a milliammeter, determine the effective value of the current in the circuit I e; using the ratio I e I m / 2 and solving it with respect to I m 2 Ie, determine the amplitude of the current in the circuit.

4. Enter the data in the table.

Reference data: active resistance of the solenoid R = 56 Ohm; solenoid length l = 40 cm; solenoid diameter d = 2 cm; the number of turns of the solenoid N = 2000.

1. Formulate the purpose of the work.

2. Define inductance?

3. What is the unit of inductance?

4. Write down the working formula for determining the inductance of the solenoid.

1. Get a formula for determining the inductance of a solenoid based on its geometric dimensions and the number of turns.

2. What is called impedance?

3. How are the maximum and effective values ​​​​of current and voltage in an alternating current circuit related?

4. Derive the working formula for the inductance of the solenoid.

5. Describe the phenomenon of self-induction.

6. What is the physical meaning of inductance?

BIBLIOGRAPHY

1. Saveliev I.G. Course of general physics. T.2, T. 4. - M .: Vyssh.

school, 2002. - 325 p.

Higher school, 1970. - 448 p.

3. Kalashnikov S.G. Electricity. - M .: Higher. school, 1977. - 378 p.

4. Trofimova T.I. Physics course. - M .: "Academy"., 2006. - 560s.

5. Purcell E. Electricity and magnetism. - M.: Nauka, 1971.p.

6. Detlaf A.A. Course of physics: Textbook for students of higher educational institutions. - M .: "Academy", 2008. - 720 p.

7. Kortnev A.V. Workshop on physics.- M.: Higher. school, 1968. p.

8. Iveronova V.I. Physical workshop. - M .: Fizmatgiz, 1962. - 956 p.

Fundamental physical constants Atomic unit a.mu. ) 10-15m 1, Compton waves K,p=h/ 1.3214099(22) 10-15m 1, Compton waves K,e=h/ 2.4263089(40) 10-12m 1, electron waves K ,e/(2) 3.8615905(64) 10-13m 1, Bohr magneton B=e/ 9.274078(36) 10-24J/T ) 10-27 J/T 3, neutron mass Electron mass 0.9109534(47) 10-30 kg of ideal gas po under normal conditions (T0=273.15 K, p0=101323 Pa) Constant Avo- 6.022045(31 ) 1023 mol- Boltzmann gas constant 8.31441(26) J/(mol K) universal gravity constant G, 6.6720(41) 10-11 N m2/kg2 5663706144 10-7H/m filament Quantum magnetic-F o = 2.0678506(54) 10-15Wb 2, radiation first radiation second radiation electric (0с2) classical (4me) standard neutron proton electron-acting 1 a.m.u. .

N o t e. Numbers in parentheses indicate the standard error in the last digits of the value given.

Introduction

Basic safety requirements for laboratory work in the educational laboratory of electricity and electromagnetism

Fundamentals of electrical measurements

Laboratory work No. 31. Measuring the value of electrical resistance using the Whitson R-bridge .................. Laboratory work No. 32. Studying the dependence of the resistance of metals on temperature

Lab #33 Determining the capacitance of a capacitor using a Wheatstone C-bridge

Laboratory work No. 34. Studying the operation of an electronic oscilloscope

Laboratory work No. 35. Studying the operation of a vacuum triode and determining its static parameters

Laboratory work No. 36. Electrical conductivity of liquids.

Determination of the Faraday number and electron charge

Laboratory work No. 37. Studying the operation mode of an RC generator using an electronic oscilloscope

Laboratory work No. 38. The study of the electrostatic field

Laboratory work No. 40. Determination of the horizontal component of the earth's magnetic field strength

Laboratory work No. 41. The study of the zener diode and the removal of its characteristics

Laboratory work No. 42. Studying a vacuum diode and determining the specific charge of an electron

Laboratory work No. 43. Studying the operation of semiconductor diodes

Laboratory work No. 45. Removing the magnetization curve and hysteresis loop using an electronic oscilloscope

Laboratory work No. 46. Damped electrical oscillations

Laboratory work No. 47. The study of forced electrical oscillations and the removal of a family of resonant curves...... Laboratory work No. 48. Measurement of resistivity

Lab #49 Determining the Inductance of a Solenoid

Bibliography

Application …………………………………………………… Dmitry Borisovich Kim Alexander Alekseevich Kropotov Lyudmila Andreevna Gerashchenko Electricity and electromagnetism Laboratory workshop Uch.-ed. l. 9.0. Conv. oven l. 9.0.

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