Oscillation, as a category of physical representations, is one of the basic concepts of physics and is defined, in general terms, as a recurring process of changing a certain physical quantity. If these changes are repeated, then this means that there is a certain period of time after which it takes the same value. This period of time is called

And actually, why fluctuations? Yes, because if you fix the value of this quantity, say at the moment T1, then at the moment Tx it will take on a different value, say, it will increase, and after a while it will increase again. But the increase cannot be eternal, because for a repeating process, there will come a moment when this physical quantity must be repeated, i.e. will again take the same value as at the moment T1, although on the time scale this is already the moment T2.

What has changed? Time. One time interval has passed, which will be repeated as a time distance between the same values ​​of a physical quantity. And what happened to the physical quantity during this period of time? Yes, it's okay, she just made one hesitation - she went through a full cycle of her changes - from the maximum to the minimum value. If in the process of changing from T1 to T2 the time was fixed, then the difference T=T2-T1 gives a numerical expression of the time period.

A good example of an oscillatory process is a spring pendulum. The weight moves up and down, the process repeats, and the value of a physical quantity, for example, the height of the pendulum, fluctuates between the maximum and minimum values.

The description of the oscillation process includes parameters that are universal for oscillations of any nature. These can be mechanical, electromagnetic vibrations, etc. At the same time, it is always important to understand that an oscillatory process for its existence necessarily includes two objects, each of which can receive and / or give energy - that's the very mechanical or electromagnetic that was discussed above. At each moment of time, one of the objects gives energy, and the second receives. At the same time, energy changes its essence into something very similar, but not the same. So, the energy of the pendulum turns into the energy of a compressed spring, and they periodically change in the process of oscillation, solving the eternal question of partnership - who should raise and lower whom, i.e. release or store energy.

Electromagnetic oscillations already in the name contain an indication of the members of the alliance - electric and and the well-known capacitor and inductance serve as the keepers of these fields. Connected into an electrical circuit, they represent an oscillatory circuit in which energy is transferred in exactly the same way as in a pendulum - the electrical energy passes into the magnetic field of the inductance and vice versa.

If the capacitor-inductance system is left to itself and electromagnetic oscillations arise in it, then their period is determined by the parameters of the system, i.e. inductance and capacitance - there are no others. Simply put, in order to “pour” energy from a source, say, a capacitor (and there is also a more accurate analogue of its name - “capacity”), into an inductance, you need to spend time proportional to the amount of stored energy, i.e. capacitance. In fact, the value of this "capacity" is the parameter on which the oscillation period depends. More capacity, more energy - longer energy transfer, longer period of electromagnetic oscillations.

What physical quantities are included in the set that determines the description in all its manifestations, including oscillatory processes? These are the components of the field: charge, magnetic induction, voltage. It should be noted that electromagnetic oscillations are the widest range of phenomena that we, as a rule, rarely connect with each other, although this is the same essence. And how do they differ? The first difference between any fluctuations is their period, the essence of which was discussed above. In technology and science, it is customary to talk about the reciprocal of the period value, frequency - the number of oscillations per second. The system unit of frequency is hertz.

So, the whole scale of electromagnetic oscillations is a sequence of frequencies of electromagnetic radiation that propagate in space.

The following areas are conditionally distinguished:

Radio waves - spectral zone from 30 kHz to 3000 GHz;

Infrared rays - a section of longer wavelength radiation than light;

visible light;

Ultraviolet rays - a section of shorter wavelength radiation than light;

X-rays;

Gamma rays.

The entire given range of radiation is electromagnetic radiation of the same nature, but of different frequencies. The breakdown into sections is purely utilitarian, which is dictated by the convenience of technical and scientific applications.

There are different types of oscillations in physics, characterized by certain parameters. Consider their main differences, classification according to various factors.

Basic definitions

By oscillation is meant a process in which, at regular intervals, the main characteristics of the movement have the same values.

Such oscillations are called periodic, in which the values ​​of the basic quantities are repeated at regular intervals (period of oscillations).

Varieties of oscillatory processes

Let us consider the main types of oscillations that exist in fundamental physics.

Free vibrations are those that occur in a system that is not subjected to external variable influences after the initial shock.

An example of free oscillations is a mathematical pendulum.

Those types of mechanical vibrations that occur in the system under the action of an external variable force.

Features of the classification

According to the physical nature, the following types of oscillatory movements are distinguished:

• mechanical;
• thermal;
• electromagnetic;
• mixed.

According to the option of interaction with the environment

Types of oscillations in interaction with the environment are divided into several groups.

Forced oscillations appear in the system under the action of an external periodic action. As examples of this type of oscillation, we can consider the movement of hands, leaves on trees.

For forced harmonic oscillations, a resonance may appear, in which, with equal values ​​of the frequency of the external action and the oscillator, with a sharp increase in amplitude.

Natural vibrations in the system under the influence of internal forces after it is taken out of equilibrium. The simplest variant of free vibrations is the movement of a load that is suspended on a thread or attached to a spring.

Self-oscillations are called types in which the system has a certain amount of potential energy used to make oscillations. Their distinctive feature is the fact that the amplitude is characterized by the properties of the system itself, and not by the initial conditions.

For random oscillations, the external load has a random value.

Basic parameters of oscillatory movements

All types of oscillations have certain characteristics, which should be mentioned separately.

Amplitude is the maximum deviation from the equilibrium position, the deviation of a fluctuating value, it is measured in meters.

The period is the time of one complete oscillation, after which the characteristics of the system are repeated, calculated in seconds.

The frequency is determined by the number of oscillations per unit of time, it is inversely proportional to the period of oscillation.

The oscillation phase characterizes the state of the system.

Characteristic of harmonic vibrations

Such types of oscillations occur according to the law of cosine or sine. Fourier managed to establish that any periodic oscillation can be represented as a sum of harmonic changes by expanding a certain function in

As an example, consider a pendulum having a certain period and cyclic frequency.

What characterizes these types of oscillations? Physics considers an idealized system, which consists of a material point, which is suspended on a weightless inextensible thread, oscillates under the influence of gravity.

Such types of vibrations have a certain amount of energy, they are common in nature and technology.

With prolonged oscillatory motion, the coordinates of its center of mass change, and with alternating current, the value of current and voltage in the circuit changes.

There are different types of harmonic oscillations according to their physical nature: electromagnetic, mechanical, etc.

As forced oscillations, the shaking of the vehicle, which moves on a rough road, acts.

The main differences between forced and free vibrations

These types of electromagnetic oscillations differ in physical characteristics. The presence of medium resistance and friction forces lead to damping of free oscillations. In the case of forced oscillations, energy losses are compensated by its additional supply from an external source.

The period of a spring pendulum relates the mass of the body and the stiffness of the spring. In the case of a mathematical pendulum, it depends on the length of the thread.

With a known period, it is possible to calculate the natural frequency of the oscillatory system.

In technology and nature, there are vibrations with different frequency values. For example, the pendulum that oscillates in St. Isaac's Cathedral in St. Petersburg has a frequency of 0.05 Hz, while for atoms it is several million megahertz.

After a certain period of time, the damping of free oscillations is observed. That is why forced oscillations are used in real practice. They are in demand in a variety of vibration machines. The vibratory hammer is a shock-vibration machine, which is intended for driving pipes, piles, and other metal structures into the ground.

Electromagnetic vibrations

Characteristics of vibration modes involves the analysis of the main physical parameters: charge, voltage, current strength. As an elementary system, which is used to observe electromagnetic oscillations, is an oscillatory circuit. It is formed by connecting a coil and a capacitor in series.

When the circuit is closed, free electromagnetic oscillations arise in it, associated with periodic changes in the electric charge on the capacitor and the current in the coil.

They are free due to the fact that when they are performed there is no external influence, but only the energy that is stored in the circuit itself is used.

In the absence of external influence, after a certain period of time, attenuation of the electromagnetic oscillation is observed. The reason for this phenomenon will be the gradual discharge of the capacitor, as well as the resistance that the coil actually has.

That is why damped oscillations occur in a real circuit. Reducing the charge on the capacitor leads to a decrease in the energy value in comparison with its original value. Gradually, it will be released in the form of heat on the connecting wires and the coil, the capacitor will be completely discharged, and the electromagnetic oscillation will be completed.

The Significance of Fluctuations in Science and Technology

Any movements that have a certain degree of repetition are oscillations. For example, a mathematical pendulum is characterized by a systematic deviation in both directions from the original vertical position.

For a spring pendulum, one complete oscillation corresponds to its movement up and down from the initial position.

In an electrical circuit that has capacitance and inductance, there is a repetition of charge on the plates of the capacitor. What is the cause of oscillatory movements? The pendulum functions due to the fact that gravity causes it to return to its original position. In the case of a spring model, a similar function is performed by the elastic force of the spring. Passing the equilibrium position, the load has a certain speed, therefore, by inertia, it moves past the average state.

Electrical oscillations can be explained by the potential difference that exists between the plates of a charged capacitor. Even when it is completely discharged, the current does not disappear, it is recharged.

In modern technology, oscillations are used, which differ significantly in their nature, degree of repetition, character, and also the "mechanism" of occurrence.

Mechanical vibrations are made by the strings of musical instruments, sea waves, and a pendulum. Chemical fluctuations associated with a change in the concentration of reactants are taken into account when conducting various interactions.

Electromagnetic oscillations make it possible to create various technical devices, for example, a telephone, ultrasonic medical devices.

Cepheid brightness fluctuations are of particular interest in astrophysics, and scientists from different countries are studying them.

Conclusion

All types of oscillations are closely related to a huge number of technical processes and physical phenomena. Their practical importance is great in aircraft construction, shipbuilding, the construction of residential complexes, electrical engineering, radio electronics, medicine, and fundamental science. An example of a typical oscillatory process in physiology is the movement of the heart muscle. Mechanical vibrations are found in organic and inorganic chemistry, meteorology, and also in many other natural sciences.

The first studies of the mathematical pendulum were carried out in the seventeenth century, and by the end of the nineteenth century, scientists were able to establish the nature of electromagnetic oscillations. The Russian scientist Alexander Popov, who is considered the "father" of radio communications, conducted his experiments precisely on the basis of the theory of electromagnetic oscillations, the results of research by Thomson, Huygens, and Rayleigh. He managed to find a practical application for electromagnetic oscillations, to use them to transmit a radio signal over a long distance.

Academician P. N. Lebedev for many years conducted experiments related to the production of high-frequency electromagnetic oscillations using alternating electric fields. Thanks to numerous experiments related to various types of oscillations, scientists have managed to find areas for their optimal use in modern science and technology.

§ 3.5. Electromagnetic oscillations and waves

Electromagnetic oscillations are periodic changes over time in electrical and magnetic quantities in an electrical circuit.

During oscillations, a continuous process of transformation of the energy of the system from one form into another takes place. In the case of oscillations of the electromagnetic field, the exchange can only take place between the electric and magnetic components of this field. The simplest system where this process can take place is an oscillatory circuit. An ideal oscillatory circuit (LC circuit) is an electrical circuit consisting of a coil with an inductance L and a capacitor C.

Unlike a real oscillatory circuit, which has electrical resistance R, the electrical resistance of an ideal circuit is always zero. Therefore, an ideal oscillatory circuit is a simplified model of a real circuit.

Consider the processes that occur in the oscillatory circuit. To bring the system out of equilibrium, we charge the capacitor so that there is a charge Q on its plates m. From the formula relating the charge of the capacitor and the voltage on it, we find the value of the maximum voltage on the capacitor
. There is no current in the circuit at this point in time, i.e.
. Immediately after the capacitor is charged, under the influence of its electric field, an electric current will appear in the circuit, the value of which will increase over time. The capacitor at this time will begin to discharge, because. the electrons that create the current (I remind you that the direction of the movement of positive charges is taken as the direction of the current) leave the negative plate of the capacitor and come to the positive one. Along with charge q tension will decrease u. With an increase in the current strength through the coil, an EMF of self-induction will occur, which prevents a change (increase) in the current strength. As a result, the current strength in the oscillatory circuit will increase from zero to a certain maximum value not instantly, but over a certain period of time, determined by the inductance of the coil. Capacitor charge q decreases and at some point in time becomes equal to zero ( q = 0, u= 0), the current in the coil will reach its maximum value I m. Without the electric field of the capacitor (and resistance), the electrons that create the current continue to move by inertia. In this case, the electrons arriving at the neutral plate of the capacitor give it a negative charge, the electrons leaving the neutral plate give it a positive charge. The capacitor begins to charge q(and voltage u), but of opposite sign, i.e. the capacitor is recharged. Now the new electric field of the capacitor prevents the electrons from moving, so the current begins to decrease. Again, this does not happen instantly, since now the self-induction EMF seeks to compensate for the decrease in current and “supports” it. And the value of the current I m turns out maximum current in contour. Further, the current strength becomes equal to zero, and the charge of the capacitor reaches its maximum value Q m (U m). And again, under the action of the electric field of the capacitor, an electric current will appear in the circuit, but directed in the opposite direction, the value of which will increase over time. And the capacitor will be discharged at this time. And so on.

Since the charge on the capacitor q(and voltage u) determines its electric field energy W e and the current in the coil is the energy of the magnetic field wm then along with changes in charge, voltage and current strength, the energies will also change.

Electromagnetic vibrations are fluctuations in electric charge, current strength, voltage, associated fluctuations in the electric field strength and magnetic field induction.

Free vibrations are those that occur in a closed system due to the deviation of this system from a state of stable equilibrium. With regard to the oscillatory circuit, this means that free electromagnetic oscillations in the oscillatory circuit occur after the energy is communicated to the system (capacitor charging or current passing through the coil).

The cyclic frequency and period of oscillations in the oscillatory circuit are determined by the formulas:
,
.

Maxwell theoretically predicted the existence of electromagnetic waves, i.e. an alternating electromagnetic field propagating in space at a finite speed, and created the electromagnetic theory of light.

An electromagnetic wave is the propagation in space over time of oscillations of vectors and .

If a rapidly changing electric field arises at any point in space, then it causes the appearance of an alternating magnetic field at neighboring points, which, in turn, excites the appearance of an alternating electric field, and so on. The faster the magnetic field changes (more ), the more intense the emerging electric field E and vice versa. Thus, a necessary condition for the formation of intense electromagnetic waves is a sufficiently high frequency of electromagnetic oscillations.

It follows from Maxwell's equations that in free space, where there are no currents and charges ( j=0, q=0) electromagnetic waves are transverse, i.e. wave velocity vector perpendicular to the vectors and , and vectors
form a right-handed triple.

M
The electromagnetic wave model is shown in the figure. This is a plane linearly polarized wave. Wavelength
, where T is the oscillation period, - oscillation frequency. In optics and radiophysics, the model of an electromagnetic wave is expressed in terms of the vectors
. From Maxwell's equations it follows
. This means that in a traveling plane electromagnetic wave, the oscillations of the vectors and occur in the same phase and at any time the electrical energy of the wave is equal to the magnetic.

The speed of an electromagnetic wave in a medium
where V is the speed of an electromagnetic wave in a given medium,
,With is the speed of an electromagnetic wave in vacuum, equal to the speed of light.

Let's derive the wave equation.

As is known from the theory of oscillations, the equation of a plane wave propagating along the x axis
, where
– fluctuating value (in this case E or H), v – wave speed, ω is the cyclic oscillation frequency.

So the wave equation
We differentiate it twice with respect to t and by x.
,
. From here we get
. Similarly, you can get
. In the general case, when the wave propagates in an arbitrary direction, these equations should be written as:
,
. Expression
is called the Laplace operator. In this way,

. These expressions are called wave equations.

In the oscillatory circuit there is a periodic conversion of the electrical energy of the capacitor
into the magnetic energy of the inductor
. Oscillation period
. In this case, the radiation of electromagnetic waves is small, because. the electric field is concentrated in the capacitor, and the magnetic field is concentrated inside the solenoid. To make the radiation noticeable, you need to increase the distance between the capacitor plates FROM and coil turns L. In this case, the volume occupied by the field will increase, L and FROM– will decrease, i.e. the oscillation frequency will increase.

Experimentally, electromagnetic waves were first obtained by Hertz (1888) using the vibrator he invented. Popov (1896) invented the radio, i.e. used electromagnetic waves to transmit information.

To characterize the energy carried by an electromagnetic wave, the energy flux density vector is introduced. It is equal to the energy carried by a wave in 1 second through a unit area perpendicular to the velocity vector .
where
is the volumetric energy density, v is the wave velocity.

Bulk energy density
is made up of the energy of the electric field and the magnetic field
.

Considering
, can be written
. Hence the energy flux density. Because the
, we get
. This is the Umov-Poynting vector.

The scale of electromagnetic waves is the arrangement of the ranges of electromagnetic waves depending on their wavelength λ and corresponding properties.

1) Radio waves. The wavelength λ is from hundreds of kilometers to centimeters. Radio equipment is used for generation and registration.

2) Microwave region λ from 10 cm to 0.1 cm. This is the radar range or the microwave (super high frequency) range. To generate and register these waves, there is a special microwave equipment.

3) Infrared (IR) region λ~1mm 800nm. Radiation sources are heated bodies. Receivers - thermal photocells, thermoelements, bolometers.

4) Visible light perceived by the human eye. λ~0.76 0.4 µm.

5) Ultraviolet (UV) region λ~400 10 nm. Sources - gas discharges. Indicators - photographic plates.

6) X-ray radiation λ~10nm 10 -3 nm. Sources - X-ray tubes. Indicators - photographic plates.

7) γ-rays λ<10пм. Источники – радиоактивные превращения. Индикаторы – специальные счетчики.

An electrical circuit consisting of an inductor and a capacitor (see figure) is called an oscillatory circuit. In this circuit, peculiar electrical oscillations can occur. Let, for example, at the initial moment of time we charge the plates of the capacitor with positive and negative charges, and then let the charges move. If the coil were not present, the capacitor would begin to discharge, an electric current would appear in the circuit for a short time, and the charges would disappear. This is where the following happens. First, due to self-induction, the coil prevents the increase in current, and then, when the current begins to decrease, it prevents its decrease, i.e. maintains current. As a result, the self-induction EMF charges the capacitor with reverse polarity: the plate that was initially positively charged acquires a negative charge, the second becomes positive. If there is no loss of electrical energy (in the case of low resistance of the circuit elements), then the magnitude of these charges will be the same as the magnitude of the initial charges of the capacitor plates. In the future, the movement of the process of moving charges will be repeated. Thus, the movement of charges in the circuit is an oscillatory process.

To solve the problems of the Unified State Examination, devoted to electromagnetic oscillations, you need to remember a number of facts and formulas regarding the oscillatory circuit. First, you need to know the formula for the oscillation period in the circuit. Secondly, to be able to apply the law of conservation of energy to the oscillatory circuit. And finally (although such tasks are rare), be able to use the dependence of the current through the coil and the voltage across the capacitor from time to time.

The period of electromagnetic oscillations in the oscillatory circuit is determined by the relation:

where and are the charge on the capacitor and the current in the coil at this point in time, and are the capacitance of the capacitor and the inductance of the coil. If the electrical resistance of the circuit elements is small, then the electrical energy of the circuit (24.2) remains practically unchanged, despite the fact that the charge of the capacitor and the current in the coil change over time. From formula (24.4) it follows that during electrical oscillations in the circuit, energy transformations occur: at those moments in time when the current in the coil is zero, the entire energy of the circuit is reduced to the energy of the capacitor. At those moments of time when the charge of the capacitor is zero, the energy of the circuit is reduced to the energy of the magnetic field in the coil. Obviously, at these moments of time, the charge of the capacitor or the current in the coil reaches its maximum (amplitude) values.

With electromagnetic oscillations in the circuit, the charge of the capacitor changes over time according to the harmonic law:

standard for any harmonic vibrations. Since the current in the coil is the derivative of the charge of the capacitor with respect to time, from formula (24.4) one can find the dependence of the current in the coil on time

In the exam in physics, tasks for electromagnetic waves are often offered. The minimum knowledge required to solve these problems includes an understanding of the basic properties of an electromagnetic wave and knowledge of the scale of electromagnetic waves. Let us briefly formulate these facts and principles.

According to the laws of the electromagnetic field, an alternating magnetic field generates an electric field, an alternating electric field generates a magnetic field. Therefore, if one of the fields (for example, electric) starts to change, a second field (magnetic) will arise, which then again generates the first (electric), then again the second (magnetic), etc. The process of mutual transformation into each other of electric and magnetic fields, which can propagate in space, is called an electromagnetic wave. Experience shows that the directions in which the vectors of the electric and magnetic field strengths fluctuate in an electromagnetic wave are perpendicular to the direction of its propagation. This means that electromagnetic waves are transverse. In Maxwell's theory of the electromagnetic field, it is proved that an electromagnetic wave is created (radiated) by electric charges as they move with acceleration. In particular, the source of an electromagnetic wave is an oscillatory circuit.

The length of an electromagnetic wave, its frequency (or period) and propagation velocity are related by a relation that is valid for any wave (see also formula (11.6)):

Electromagnetic waves in vacuum propagate at a speed = 3 10 8 m/s, the speed of electromagnetic waves in the medium is less than in vacuum, and this speed depends on the frequency of the wave. This phenomenon is called wave dispersion. An electromagnetic wave has all the properties of waves propagating in elastic media: interference, diffraction, and the Huygens principle is valid for it. The only thing that distinguishes an electromagnetic wave is that it does not need a medium to propagate - an electromagnetic wave can also propagate in a vacuum.

In nature, electromagnetic waves are observed with very different frequencies from each other, and due to this, they have significantly different properties (despite the same physical nature). The classification of the properties of electromagnetic waves depending on their frequency (or wavelength) is called the scale of electromagnetic waves. We give a brief overview of this scale.

Electromagnetic waves with a frequency less than 10 5 Hz (ie, with a wavelength greater than a few kilometers) are called low-frequency electromagnetic waves. Most household electrical appliances emit waves of this range.

Waves with a frequency of 10 5 to 10 12 Hz are called radio waves. These waves correspond to wavelengths in vacuum from several kilometers to several millimeters. These waves are used for radio communications, television, radar, cell phones. The sources of radiation of such waves are charged particles moving in electromagnetic fields. Radio waves are also emitted by free metal electrons, which oscillate in an oscillatory circuit.

The region of the scale of electromagnetic waves with frequencies lying in the range 10 12 - 4.3 10 14 Hz (and wavelengths from a few millimeters to 760 nm) is called infrared radiation (or infrared rays). Molecules of a heated substance serve as a source of such radiation. A person emits infrared waves with a wavelength of 5 - 10 microns.

Electromagnetic radiation in the frequency range 4.3 10 14 - 7.7 10 14 Hz (or wavelengths 760 - 390 nm) is perceived by the human eye as light and is called visible light. Waves of different frequencies within this range are perceived by the eye as having different colors. The wave with the smallest frequency from the visible range 4.3 10 14 is perceived as red, with the highest frequency within the visible range 7.7 10 14 Hz - as violet. Visible light is emitted during the transition of electrons in atoms, molecules of solids heated to 1000 ° C or more.

Waves with a frequency of 7.7 10 14 - 10 17 Hz (wavelength from 390 to 1 nm) are commonly called ultraviolet radiation. Ultraviolet radiation has a pronounced biological effect: it can kill a number of microorganisms, it can cause increased pigmentation of human skin (tanning), and in case of excessive exposure, in some cases it can contribute to the development of oncological diseases (skin cancer). Ultraviolet rays are contained in the radiation of the Sun, they are created in laboratories with special gas-discharge (quartz) lamps.

Beyond the region of ultraviolet radiation lies the region of X-rays (frequency 10 17 - 10 19 Hz, wavelength from 1 to 0.01 nm). These waves are emitted during deceleration in the matter of charged particles accelerated by a voltage of 1000 V or more. They have the ability to pass through thick layers of matter that are opaque to visible light or ultraviolet radiation. Due to this property, X-rays are widely used in medicine for diagnosing bone fractures and a number of diseases. X-rays have a detrimental effect on biological tissues. Due to this property, they can be used to treat oncological diseases, although when exposed to excessive radiation, they are deadly to humans, causing a number of disorders in the body. Due to the very short wavelength, the wave properties of X-rays (interference and diffraction) can only be detected on structures comparable to the size of atoms.

Gamma radiation (-radiation) is called electromagnetic waves with a frequency greater than 10 20 Hz (or a wavelength less than 0.01 nm). Such waves arise in nuclear processes. A feature of -radiation is its pronounced corpuscular properties (i.e., this radiation behaves like a stream of particles). Therefore, radiation is often referred to as a stream of -particles.

AT task 24.1.1 to establish correspondence between units of measurement, we use formula (24.1), from which it follows that the period of oscillations in a circuit with a capacitor with a capacity of 1 F and an inductance of 1 H is equal to seconds (the answer 1 ).

From the chart given in task 24.1.2, we conclude that the period of electromagnetic oscillations in the circuit is 4 ms (the response 3 ).

According to the formula (24.1) we find the oscillation period in the circuit given in task 24.1.3:
(answer 4 ). Note that according to the scale of electromagnetic waves, such a circuit emits waves of the long-wave radio range.

The period of oscillation is the time of one complete oscillation. This means that if at the initial moment of time the capacitor is charged with the maximum charge ( task 24.1.4), then after half a period the capacitor will also be charged with the maximum charge, but with reverse polarity (the plate that was initially positively charged will be negatively charged). And the maximum current in the circuit will be achieved between these two moments, i.e. in a quarter of the period (answer 2 ).

If the inductance of the coil is quadrupled ( task 24.1.5), then according to formula (24.1) the oscillation period in the circuit will double, and the frequency doubled (answer 2 ).

According to formula (24.1), with a fourfold increase in the capacitance of the capacitor ( task 24.1.6) the oscillation period in the circuit is doubled (the answer 1 ).

When the key is closed ( task 24.1.7) in the circuit, instead of one capacitor, two of the same capacitors connected in parallel will work (see figure). And since when the capacitors are connected in parallel, their capacitances add up, the closure of the key leads to a twofold increase in the capacitance of the circuit. Therefore, from formula (24.1) we conclude that the oscillation period increases by a factor (the answer is 3 ).

Let the charge on the capacitor oscillate with a cyclic frequency ( task 24.1.8). Then, according to formulas (24.3) - (24.5), the current in the coil will oscillate with the same frequency. This means that the dependence of the current on time can be represented as . From here we find the dependence of the energy of the magnetic field of the coil on time

It follows from this formula that the energy of the magnetic field in the coil oscillates with twice the frequency, and, therefore, with a period that is half the period of the charge and current oscillations (the answer is 1 ).

AT task 24.1.9 we use the law of conservation of energy for the oscillatory circuit. From formula (24.2) it follows that for the amplitude values ​​of the voltage across the capacitor and the current in the coil, the relation

where and are the amplitude values ​​of the capacitor charge and the current in the coil. From this formula, using relation (24.1) for the oscillation period in the circuit, we find the amplitude value of the current

answer 3 .

Radio waves are electromagnetic waves with specific frequencies. Therefore, the speed of their propagation in vacuum is equal to the speed of propagation of any electromagnetic waves, and in particular, X-rays. This speed is the speed of light ( task 24.2.1- answer 1 ).

As stated earlier, charged particles emit electromagnetic waves when moving with acceleration. Therefore, the wave is not emitted only with uniform and rectilinear motion ( task 24.2.2- answer 1 ).

An electromagnetic wave is an electric and magnetic field that varies in space and time in a special way and supports each other. Therefore the correct answer is task 24.2.3 - 2 .

From the given in the condition tasks 24.2.4 It follows from the graph that the period of this wave is - = 4 μs. Therefore, from formula (24.6) we obtain m (the answer 1 ).

AT task 24.2.5 by formula (24.6) we find

(answer 4 ).

An oscillatory circuit is connected to the antenna of the electromagnetic wave receiver. The electric field of the wave acts on the free electrons in the circuit and causes them to oscillate. If the frequency of the wave coincides with the natural frequency of electromagnetic oscillations, the amplitude of oscillations in the circuit increases (resonance) and can be registered. Therefore, to receive an electromagnetic wave, the frequency of natural oscillations in the circuit must be close to the frequency of this wave (the circuit must be tuned to the frequency of the wave). Therefore, if the circuit needs to be reconfigured from a wave length of 100 m to a wave length of 25 m ( task 24.2.6), the natural frequency of electromagnetic oscillations in the circuit must be increased by 4 times. To do this, according to formulas (24.1), (24.4), the capacitance of the capacitor should be reduced by 16 times (the answer 4 ).

According to the scale of electromagnetic waves (see the introduction to this chapter), the maximum length of those listed in the condition tasks 24.2.7 electromagnetic waves has radiation from the antenna of a radio transmitter (response 4 ).

Among those listed in task 24.2.8 electromagnetic waves, X-ray radiation has a maximum frequency (response 2 ).

The electromagnetic wave is transverse. This means that the vectors of the electric field strength and magnetic field induction in the wave at any time are directed perpendicular to the direction of wave propagation. Therefore, when the wave propagates in the direction of the axis ( task 24.2.9), the electric field strength vector is directed perpendicular to this axis. Therefore, its projection on the axis is necessarily equal to zero = 0 (answer 3 ).

The propagation speed of an electromagnetic wave is an individual characteristic of each medium. Therefore, when an electromagnetic wave passes from one medium to another (or from vacuum to a medium), the speed of the electromagnetic wave changes. And what can be said about the other two parameters of the wave included in the formula (24.6) - the wavelength and frequency. Will they change when the wave passes from one medium to another ( task 24.2.10)? Obviously, the wave frequency does not change when moving from one medium to another. Indeed, a wave is an oscillatory process in which an alternating electromagnetic field in one medium creates and maintains a field in another medium due to precisely these changes. Therefore, the periods of these periodic processes (and hence the frequencies) in one and the other medium must coincide (the answer is 3 ). And since the speed of the wave in different media is different, it follows from the reasoning and formula (24.6) that the wavelength changes when it passes from one medium to another.

In electrical circuits, as well as in mechanical systems such as a spring weight or a pendulum, free vibrations.

Electromagnetic vibrationscalled periodic interrelated changes in charge, current and voltage.

Freeoscillations are called those that occur without external influence due to the initially accumulated energy.

compelledare called oscillations in the circuit under the action of an external periodic electromotive force

Free electromagnetic oscillations are periodically repeating changes in electromagnetic quantities (q- electric charge,I- current strength,U- potential difference) occurring without energy consumption from external sources.

The simplest electrical system that can oscillate freely is serial RLC loop or oscillatory circuit.

Oscillatory circuit -is a system consisting of series-connected capacitance capacitorsC, inductorsL and a conductor with resistanceR

Consider a closed oscillatory circuit consisting of an inductance L and containers FROM.

To excite oscillations in this circuit, it is necessary to inform the capacitor of a certain charge from the source ε . When the key K is in position 1, the capacitor is charged to voltage. After switching the key to position 2, the process of discharging the capacitor through the resistor begins R and an inductor L. Under certain conditions, this process can be oscillatory.

Free electromagnetic oscillations can be observed on the oscilloscope screen.

As can be seen from the oscillation graph obtained on the oscilloscope, free electromagnetic oscillations are fading, i.e., their amplitude decreases with time. This is because part of the electrical energy on the active resistance R is converted into internal energy. conductor (the conductor heats up when an electric current passes through it).

Let us consider how oscillations occur in an oscillatory circuit and what changes in energy occur in this case. Let us first consider the case when there are no losses of electromagnetic energy in the circuit ( R = 0).

If you charge the capacitor to a voltage U 0, then at the initial time t 1 =0, the amplitude values ​​of the voltage U 0 and charge q 0 = CU 0 will be established on the capacitor plates.

The total energy W of the system is equal to the energy of the electric field W el:

If the circuit is closed, then current begins to flow. Emf appears in the circuit. self-induction

Due to self-induction in the coil, the capacitor is not discharged instantly, but gradually (since, according to the Lenz rule, the resulting inductive current with its magnetic field counteracts the change in the magnetic flux by which it is caused. That is, the magnetic field of the inductive current does not allow the magnetic flux of the current to instantly increase in the contour). In this case, the current increases gradually, reaching its maximum value I 0 at time t 2 =T/4, and the charge on the capacitor becomes equal to zero.

As the capacitor discharges, the energy of the electric field decreases, but at the same time the energy of the magnetic field increases. The total energy of the circuit after discharging the capacitor is equal to the energy of the magnetic field W m:

At the next moment in time, the current flows in the same direction, decreasing to zero, which causes the capacitor to recharge. The current does not stop instantly after the capacitor is discharged due to self-induction (now the magnetic field of the induction current does not allow the magnetic flux of the current in the circuit to decrease instantly). At the time t 3 \u003d T / 2, the capacitor charge is again maximum and equal to the initial charge q \u003d q 0, the voltage is also equal to the initial U \u003d U 0, and the current in the circuit is zero I \u003d 0.

Then the capacitor discharges again, the current flows through the inductor in the opposite direction. After a period of time T, the system returns to its initial state. Complete oscillation is completed, the process is repeated.

The graph of change in charge and current strength with free electromagnetic oscillations in the circuit shows that the current strength fluctuations lag behind the charge fluctuations by π/2.

At any given time, the total energy is:

With free vibrations, a periodic transformation of electrical energy occurs W e, stored in the capacitor, into magnetic energy W m coil and vice versa. If there are no energy losses in the oscillatory circuit, then the total electromagnetic energy of the system remains constant.

Free electrical vibrations are similar to mechanical vibrations. The figure shows graphs of charge change q(t) capacitor and bias x(t) load from the equilibrium position, as well as current graphs I(t) and load speed υ( t) for one period of oscillation.

In the absence of damping, free oscillations in an electrical circuit are harmonic, that is, they occur according to the law

q(t) = q 0 cos(ω t + φ 0)

Options L and C oscillatory circuit determine only the natural frequency of free oscillations and the period of oscillations - Thompson's formula

Amplitude q 0 and initial phase φ 0 are determined initial conditions, that is, the way in which the system was brought out of equilibrium.

For fluctuations in charge, voltage and current, formulas are obtained:

For a capacitor:

q(t) = q 0 cosω 0 t

U(t) = U 0 cosω 0 t

For an inductor:

i(t) = I 0 cos(ω 0 t+ π/2)

U(t) = U 0 cos(ω 0 t + π)

Let's remember main characteristics of oscillatory motion:

q 0, U 0 , I 0 - amplitude is the modulus of the largest value of the fluctuating quantity

T - period- the minimum time interval after which the process is completely repeated

ν - Frequency- the number of oscillations per unit time

ω - Cyclic frequency is the number of oscillations in 2n seconds

φ - oscillation phase- the value standing under the cosine (sine) sign and characterizing the state of the system at any time.