Magnetic field strength- (standard designation H) is a vector physical quantity equal to the difference of the magnetic induction vector B and the magnetization vector M.
In SI: , where μ 0 is the magnetic constant
What is the induction of a magnetic field, the relationship with the strength of the magnetic field in the void.
Magnetic induction- vector quantity, which is a force characteristic of the magnetic field (its action on charged particles) at a given point in space. Determines the force with which the magnetic field acts on a charge moving at a speed. SI units: T
What units of measure for magnetic field induction do you know?
Tesla(Russian designation: Tl; international designation: T) is the SI unit of magnetic field induction.
Through other SI units, 1 Tesla is expressed as follows:
V s / m²
N A −1 m −1
What is magnetic flux, how is it measured?
magnetic flux- flux as an integral of the magnetic induction vector through the finite surface . Defined via the integral over the surface
In SI, the unit of magnetic flux is Weber (Wb, dimension - V s \u003d kg m² s −2 A −1),
Formulate the law of electromagnetic induction (according to Maxwell)
Any change in the magnetic field generates a vortex electric field in the surrounding space, the lines of force of which are closed.
Maxwell hypothesized the existence of the reverse process as well:
The time-varying electric field generates a magnetic field in the surrounding space.
20. How is the law of electromagnetic induction formulated according to Ampere's experiments? Ampère experience installed interaction of conductors with current, attraction of parallel conductors with current in one direction and repulsion with the opposite. The strength of the interaction grew with the current, the length of the conductors and their rotation to the field, as ampere powerF A \u003d IВlsin a. Here B=Fmax /Il-magnetic field induction(from lat. inductio - guidance) - the maximum force acting on a conductor 1 m long with a current of 1 A. It characterizes magnetism in "tesla", [B] = 1N / 1A. 1m=1Tl (N.Tesla - Serbian inventor of electrical engineering). The induction of ordinary magnets is less than 0.01 T, the Earth's is 10 -5 T, and much more on the Sun and stars. The direction of induction indicates the northern end of the magnetic needle, outside the magnet from pole C to S, current - clockwise.
What is electromotive force and how is it measured?
Electromotive force(EMF) - a physical quantity that characterizes the work of external (non-potential) forces in sources of direct or alternating current. In a closed conducting circuit, the EMF is equal to the work of these forces in moving a single positive charge along the circuit.
EMF is measured, like voltage, in volts.
What is the essence of Lenz's rule?
Lenz's rule, a rule for determining the direction induction current: The inductive current that occurs when the relative movement of the conducting circuit and the source of the magnetic field always has such a direction that its own magnetic flux compensates for changes in the external magnetic flux that caused this current.
What is active electrical resistance?
Electrical resistance- a physical quantity that characterizes the properties of a conductor to prevent the passage of electric current and is equal to the ratio of the voltage at the ends of the conductor to the strength of the current flowing through it. Resistance for AC circuits and for alternating electromagnetic fields is described in terms of impedance and wave resistance. Resistance (resistor) is also called a radio component designed to be introduced into electrical circuits of active resistance.
Active, or resistive, resistance is possessed by a circuit element in which an irreversible process of converting electrical energy into thermal energy takes place.
What is electrical capacitance?
Electric capacity- a characteristic of a conductor, a measure of its ability to accumulate an electric charge. where Q- charge, U- conductor potential.
What is inductance?
Inductance(or self-induction coefficient) - coefficient of proportionality between the electric current flowing in any closed circuit and the magnetic flux created by this current through the surface, the edge of which is this circuit. - magnetic flux, I- current in the circuit, L- inductance.
An electric charge placed at some point in space changes the properties of that space. That is, the charge generates an electric field around itself. An electrostatic field is a special kind of matter.
The electrostatic field does not change with time.
The power characteristic of the electric field is the intensity
The electric field strength at a given point is a vector physical quantity numerically equal to the force acting on a unit positive charge placed at a given point of the field.
If a trial charge is acted upon by forces from several charges, then these forces are independent by the principle of superposition of forces, and the resultant of these forces is equal to the vector sum of the forces. The principle of superposition (superposition) of electric fields: The electric field strength of a system of charges at a given point in space is equal to the vector sum of the electric field strengths created at a given point in space by each charge of the system separately:or
The electric field is conveniently represented graphically using lines of force.
Lines of force (lines of electric field intensity) are lines, tangents to which at each point of the field coincide with the direction of the vector of intensity at a given point.
The lines of force start on a positive charge and end on a negative one (Force lines of electrostatic fields of point charges.).
The density of the lines of tension characterizes the field strength (the denser the lines are, the stronger the field).
The electrostatic field of a point charge is non-uniform (the field is stronger closer to the charge).Lines of force of electrostatic fields of infinite uniformly charged planes.
The electrostatic field of infinite uniformly charged planes is uniform. An electric field whose intensity is the same at all points is called homogeneous.
Force lines of electrostatic fields of two point charges.
Potential - energy characteristic of the electric field.
Potential- a scalar physical quantity equal to the ratio of the potential energy that an electric charge has at a given point in the electric field to the magnitude of this charge.Potential shows what potential energy will have a unit positive charge placed at a given point in the electric field. φ=W/q
where φ is the potential at a given point of the field, W is the potential energy of the charge at a given point of the field.
For the unit of measurement of potential in the SI system, take [φ] = V(1V = 1J/C)
The unit of potential is taken as the potential at such a point, to move to which from infinity an electric charge of 1 C, it is required to do work equal to 1 J.
Considering the electric field created by the system of charges, one should use to determine the field potential superposition principle:
The potential of the electric field of a system of charges at a given point in space is equal to the algebraic sum of the potentials of the electric fields created at a given point in space by each charge of the system separately:
An imaginary surface in which the potential takes the same value at all points is called equipotential surface. When moving an electric charge from point to point along the equipotential surface, its energy does not change. An infinite number of equipotential surfaces for a given electrostatic field can be constructed.
The intensity vector at each point of the field is always perpendicular to the equipotential surface drawn through the given point of the field.
ELECTRIC CHARGE. ELEMENTARY PARTICLES.
Electric charge q - physical quantity that determines the intensity of electromagnetic interaction.
[q] = l Cl (Coulomb).
Atoms are made up of nuclei and electrons. The nucleus contains positively charged protons and uncharged neutrons. Electrons carry a negative charge. The number of electrons in an atom is equal to the number of protons in the nucleus, so the atom as a whole is neutral.
The charge of any body: q = ±Ne, where e \u003d 1.6 * 10 -19 C is the elementary or minimum possible charge (electron charge), N- the number of excess or missing electrons. In a closed system, the algebraic sum of the charges remains constant:
q 1 + q 2 + … + q n = const.
A point electric charge is a charged body whose dimensions are many times smaller than the distance to another electrified body interacting with it.
Coulomb's Law
Two fixed point electric charges in vacuum interact with forces directed along a straight line connecting these charges; the modules of these forces are directly proportional to the product of the charges and inversely proportional to the square of the distance between them:
Proportionality factor
where is the electric constant.
where 12 is the force acting from the second charge to the first, and 21 - from the first to the second.
ELECTRIC FIELD. TENSION
The fact of the interaction of electric charges at a distance can be explained by the presence of an electric field around them - a material object, continuous in space and capable of acting on other charges.
The field of motionless electric charges is called electrostatic.
The characteristic of the field is its strength.
Electric field strength at a given point is a vector whose modulus is equal to the ratio of the force acting on a point positive charge to the magnitude of this charge, and the direction coincides with the direction of the force.
Field strength of a point charge Q on distance r from it is equal to
Principle of superposition of fields
The field strength of the system of charges is equal to the vector sum of the field strengths of each of the charges of the system:
The dielectric constant medium is equal to the ratio of field strengths in vacuum and in matter:
It shows how many times the substance weakens the field. Coulomb's law for two point charges q and Q located at a distance r in a medium with a permittivity:
Field strength at a distance r from charge Q is equal to
POTENTIAL ENERGY OF A CHARGED BODY IN A HOMOGENEOUS ELECTRIC STATIC FIELD
Between two large plates, charged with opposite signs and located in parallel, we place a point charge q.
Since the electric field between the plates with intensity is uniform, then the force acts on the charge at all points F = qE, which, when a charge moves a distance along, does work
This work does not depend on the shape of the trajectory, that is, when moving the charge q along an arbitrary line L work will be the same.
The work of an electrostatic field in moving a charge does not depend on the shape of the trajectory, but is determined exclusively by the initial and final states of the system. It, as in the case of the gravity field, is equal to the change in potential energy, taken with the opposite sign:
From a comparison with the previous formula, it can be seen that the potential energy of a charge in a uniform electrostatic field is:
Potential energy depends on the choice of the zero level and therefore has no deep meaning by itself.
ELECTROSTATIC FIELD POTENTIAL AND VOLTAGE
Potential a field is called, the work of which, when moving from one point of the field to another, does not depend on the shape of the trajectory. Potential are the gravity field and the electrostatic field.
The work done by the potential field is equal to the change in the potential energy of the system, taken with the opposite sign:
Potential- the ratio of the potential energy of the charge in the field to the value of this charge:
The potential of the homogeneous field is equal to
where d- distance counted from some zero level.
Potential charge interaction energy q is equal to the field.
Therefore, the work of the field to move the charge from a point with a potential φ 1 to a point with a potential φ 2 is:
The value is called the potential difference or voltage.
The voltage or potential difference between two points is the ratio of the work of the electric field to move the charge from the starting point to the final point to the value of this charge:
[U]=1J/Cl=1V
FIELD STRENGTH AND POTENTIAL DIFFERENCE
When moving charge q along the line of force of the electric field with a strength over a distance Δ d, the field does work
Since, by definition, we get:
Hence, the electric field strength is equal to
So, the strength of the electric field is equal to the change in potential when moving along the line of force per unit length.
If a positive charge moves in the direction of the field line, then the direction of the force coincides with the direction of movement, and the work of the field is positive:
Then , that is, the tension is directed in the direction of decreasing potential.
Tension is measured in volts per meter:
[E]=1 B/m
The field strength is 1 V/m if the voltage between two points of the field line, located at a distance of 1 m, is 1 V.
ELECTRIC CAPACITY
If we independently measure the charge Q, reported to the body, and its potential φ, it can be found that they are directly proportional to each other:
The value C characterizes the ability of the conductor to accumulate an electric charge and is called the electric capacitance. The capacitance of a conductor depends on its size, shape, and the electrical properties of the medium.
The electrical capacity of two conductors is the ratio of the charge of one of them to the potential difference between them:
body capacity is 1 F if, when a charge of 1 C is imparted to it, it acquires a potential of 1 V.
CAPACITORS
Capacitor- two conductors separated by a dielectric, which serve to accumulate an electric charge. The charge of a capacitor is understood as the charge modulus of one of its plates or plates.
The ability of a capacitor to store a charge is characterized by an electrical capacity, which is equal to the ratio of the capacitor's charge to the voltage:
The capacitance of a capacitor is 1 F if, at a voltage of 1 V, its charge is 1 C.
The capacitance of a flat capacitor is directly proportional to the area of the plates S, the permittivity of the medium, and is inversely proportional to the distance between the plates d:
ENERGY OF A CHARGED CAPACITOR.
Precise experiments show that W=CU 2 /2
Because q=CU, then
Electric field energy density
where V=Sd is the volume occupied by the field inside the capacitor. Given that the capacitance of a flat capacitor
and the tension on its linings U=Ed
we get:
Example. An electron, moving in an electric field from point 1 through point 2, increased its speed from 1000 to 3000 km/s. Determine the potential difference between points 1 and 2.
Coulomb's law:
where F is the force of interaction of two point charges q 1 and q 2; r is the distance between charges; is the dielectric constant of the medium; 0 - electrical constant
.
The law of conservation of charge:
,
where 
is the algebraic sum of the charges included in the isolated system; n is the number of charges.
Strength and potential of the electrostatic field:
;
, or 
,
where 
is the force acting on a point positive charge q 0 placed at a given point of the field; P is the potential energy of the charge; And ∞ is the work spent on moving the charge q 0 from a given point of the field to infinity.
Tension Vector Flow 
electric field:
a) through an arbitrary surface S placed in an inhomogeneous field:
, or 
,
where is the angle between the intensity vector 
and normal 
to the surface element; dS is the area of the surface element; E n is the projection of the stress vector onto the normal;
b) through a flat surface placed in a uniform electric field:
.
Tension Vector Flow 
through a closed surface
(integration is carried out over the entire surface).
Ostrogradsky-Gauss theorem. The flow of the intensity vector through any closed surface covering the charges q1, q2, ..., qn, -
,
where 
is the algebraic sum of charges enclosed inside a closed surface; n is the number of charges.
The intensity of the electrostatic field created by a point charge q at a distance r from the charge, -
.
The strength of the electric field created by a sphere having a radius R and carrying a charge q, at a distance r from the center of the sphere is as follows:
inside the sphere (r R) E=0;
on the surface of the sphere (r=R) 
;
outside the sphere (r R) 
.
The principle of superposition (superposition) of electrostatic fields, according to which the intensity 
of the resulting field created by two (or more) point charges is equal to the vector (geometric) sum of the strengths of the added fields, is expressed by the formula
In the case of two electric fields with strengths 
and 
the absolute value of the intensity vector is
where is the angle between the vectors 
and 
.
The intensity of the field created by an infinitely long and uniformly charged thread (or cylinder) at a distance r from its axis is
,
where is the linear charge density.
The linear charge density is a value equal to its ratio to the length of the thread (cylinder):
.
The intensity of the field created by an infinite uniformly charged plane is
,
where is the surface charge density.
The surface charge density is a value equal to the ratio of the charge distributed over the surface to its area:
.
The intensity of the field created by two infinite and parallel planes, charged uniformly and differently, with the same absolute value of the surface density of the charge (the field of a flat capacitor) -
.
The above formula is valid when calculating the field strength between the plates of a flat capacitor (in its middle part) only if the distance between the plates is much less than the linear dimensions of the capacitor plates.
electrical displacement 
associated with tension 
electric field ratio
,
which is valid only for isotropic dielectrics.
The potential of an electric field is a quantity equal to the ratio of potential energy and a point positive charge placed at a given point in the field:
.
In other words, the electric field potential is a value equal to the ratio of the work of the field forces to move a point positive charge from a given point of the field to infinity to the value of this charge:
.
The potential of the electric field at infinity is conditionally taken equal to zero.
The potential of the electric field created by a point charge q on
distance r from the charge, –
.
The potential of the electric field created by a metal sphere having a radius R and carrying a charge q, at a distance r from the center of the sphere is as follows:
inside the sphere (r R) 
;
on the surface of a sphere (r = R) 
;
outside the sphere (r R) 
.
In all formulas given for the potential of a charged sphere, is the permittivity of a homogeneous infinite dielectric surrounding the sphere.
The potential of the electric field formed by a system of n point charges at a given point, in accordance with the principle of superposition of electric fields, is equal to the algebraic sum of the potentials 
, created by individual point charges 
:
.
Energy W of interaction of a system of point charges 
is determined by the work that this system can do when they are removed relative to each other to infinity, and is expressed by the formula
,
where 
- field potential created by all (n-1) charges (except for the i-th) at the point where the charge is located 
.
The potential is related to the electric field strength by the relation
.
In the case of an electric field with spherical symmetry, this relationship is expressed by the formula
,
or in scalar form
.
In the case of a homogeneous field, i.e. field, the intensity of which at each of its points is the same both in absolute value and in direction, -
,
where 1 and 2 are the potentials of the points of two equipotential surfaces; d is the distance between these surfaces along the electric line of force.
The work done by the electric field when moving a point charge q from one point of the field, having a potential 1, to another, having a potential 2, is equal to
, or 
,
where E 
is the vector projection 
to the direction of movement; 
- movement.
In the case of a homogeneous field, the last formula takes the form
,
where 
- displacement; - angle between vector directions 
and moving 
.
A dipole is a system of two point (equal in absolute value and opposite in sign) charges located at some distance from each other.
Electric moment 
dipole is a vector directed from a negative charge to a positive one, equal to the product of the charge 
per vector 
, drawn from a negative charge to a positive one, and called the dipole arm, i.e.
.
A dipole is called a point dipole if its arm 
much less than the distance r from the center of the dipole to the point at which we are interested in the action of the dipole ( 
r), see fig. one.
Field strength of a point dipole:
,
where p is the electric moment of the dipole; r is the absolute value of the radius vector drawn from the center of the dipole to the point where the field strength is of interest to us; - angle between the radius vector 
and shoulder 
dipole.
Field strength of a point dipole at a point lying on the axis of the dipole
(=0), is found by the formula
;
at a point perpendicular to the dipole arm reconstructed from its middle 
, - according to the formula
.
The field potential of a point dipole at a point lying on the dipole axis (=0) is
,
and at a point lying on the perpendicular to the dipole arm, reconstructed from its middle 
,
–
The strength and potential of a non-point dipole are determined in the same way as for a system of charges.
The mechanical moment acting on a dipole with an electric moment p, placed in a uniform electric field with a strength E, is
, or 
,
where is the angle between the directions of the vectors 
and 
.
The capacitance of a solitary conductor or capacitor is
,
where q is the charge imparted to the conductor; 
is the change in potential caused by this charge.
The capacitance of a solitary conducting sphere of radius R, located in an infinite medium with a permittivity , is
.
If the sphere is hollow and filled with a dielectric, then its capacitance does not change.
Electric capacitance of a flat capacitor:
,
where S is the area of each capacitor plate; d is the distance between the plates; - permittivity of the dielectric filling the space between the plates.
The capacitance of a flat capacitor filled with n layers of dielectric with thickness d i and permittivity i each (layered capacitor) is
.
The capacitance of a spherical capacitor (two concentric spheres with a radius R 1 and R 2, the space between which is filled with a dielectric with a permittivity ) is as follows:
.
The capacitance of series-connected capacitors is:
in general -
,
where n is the number of capacitors;
in the case of two capacitors -
;
.
The capacitance of capacitors connected in parallel is determined as follows:
in general -
C \u003d C 1 + C 2 + ... + C n;
in the case of two capacitors -
C \u003d C 1 + C 2;
in the case of n identical capacitors with electrical capacity C 1 each -
The energy of a charged conductor is expressed in terms of charge q, potential and electrical capacity C of the conductor as follows:
.
The energy of a charged capacitor is
,
where q is the charge of the capacitor; C is the capacitance of the capacitor; U is the potential difference on its plates.
Before figuring out how to determine the strength of an electric field, it is imperative to understand the essence of this phenomenon.
Electric field properties
Mobile and immobile charges are involved in the creation of an electric field. The presence of the field is manifested in its forceful effect on them. In addition, the field is capable of creating the induction of charges located on the surface of the conductors. When a field is generated by stationary charges, it is considered a stationary electric field. Another name is electrostatic field. It is one of the varieties of the electromagnetic field, with the help of which all force interactions that occur between charged particles occur.
What is the electric field strength measured in
Tension - is a vector quantity that has a force effect on charged particles. The value is defined as the ratio of the force directed from its side to the value of a point test electric charge at a specific point of this field. A trial electric charge is introduced into the electric field on purpose so that the intensity can be calculated.
In addition to theory, there are practical ways to determine the electric field strength:
- In an arbitrary electric field, it is necessary to take a body containing an electric charge. The dimensions of this body must be smaller than the dimensions of the body with which the electric field is generated. For this purpose, you can use a small metal ball with an electric charge. It is necessary to measure the charge of the ball with an electrometer and place it in the field. The force acting on the ball must be balanced with a dynamometer. After that, readings expressed in Newtons are taken from the dynamometer. If the value of the force is divided by the value of the charge, then the value of the tension, expressed in volts / meter, will be obtained.
- The field strength at a certain point, remote from the charge at any length, is first determined by measuring the distance between them. Then, the value is divided by the resulting distance, squared. The coefficient 9*10^9 is applied to the result.
- In a capacitor, the determination of tension begins with measuring the voltage between its plates using a voltmeter. Next, you need to measure the distance between the plates. The value in volts is divided by the distance between the plates in meters. The result obtained will be the value of the electric field strength.
