Magnetic field theory and interesting facts about the earth's magnetic field. Magnetic field and its properties
Determination of the magnetic field. His sources
Definition
A magnetic field is one of the forms of an electromagnetic field that acts only on moving bodies that have an electric charge or magnetized bodies, regardless of their movement.
The sources of this field are direct electric currents, moving electric charges (bodies and particles), magnetized bodies, alternating electric fields. Sources of a constant magnetic field are direct currents.
Magnetic field properties
At a time when the study of magnetic phenomena had just begun, researchers paid special attention to the existence of poles in magnetized bars. In them, the magnetic properties were especially pronounced. It was clearly seen that the poles of the magnet are different. Opposite poles attracted, and like poles repelled. Hilbert expressed the idea of the existence of "magnetic charges". These representations were supported and developed by Coulomb. On the basis of Coulomb's experiments, the force characteristic of the magnetic field became the force with which the magnetic field acts on a magnetic charge equal to unity. Coulomb drew attention to the essential differences between the phenomena in electricity and magnetism. The difference is already manifested in the fact that electric charges can be divided and bodies with an excess of positive or negative charge can be obtained, while it is impossible to separate the north and south poles of a magnet and get a body with only one pole. From the impossibility of dividing the magnet into exclusively "northern" or "southern" Coulomb decided that these two types of charges are inseparable in each elementary particle of the magnetizing substance. Thus, it was recognized that each particle of matter - an atom, a molecule, or a group of them - is something like a micro magnet with two poles. The magnetization of the body in this case is the process of orientation of its elementary magnets under the influence of an external magnetic field (analogous to the polarization of dielectrics).
The interaction of currents is realized by means of magnetic fields. Oersted discovered that a magnetic field is excited by a current and has an orienting effect on a magnetic needle. Oersted's conductor with current was located above the magnetic needle, which could rotate. When the current flowed in the conductor, the arrow turned perpendicular to the wire. A change in the direction of the current caused a reorientation of the arrow. It followed from Oersted's experiment that the magnetic field has a direction and must be characterized by a vector quantity. This quantity was called magnetic induction and denoted: $\overrightarrow(B).$ $\overrightarrow(B)$ is similar to the intensity vector for the electric field ($\overrightarrow(E)$). The analogue of the displacement vector $\overrightarrow(D)\$ for the magnetic field is the vector $\overrightarrow(H)$, called the vector of the magnetic field strength.
A magnetic field only affects a moving electric charge. A magnetic field is generated by moving electric charges.
The magnetic field of a moving charge. The magnetic field of a coil with current. Superposition principle
The magnetic field of an electric charge that moves at a constant speed has the form:
\[\overrightarrow(B)=\frac((\mu )_0)(4\pi )\frac(q\left[\overrightarrow(v)\overrightarrow(r)\right])(r^3)\left (1\right),\]
where $(\mu )_0=4\pi \cdot (10)^(-7)\frac(H)(m)(v\SI)$ is the magnetic constant, $\overrightarrow(v)$ is the velocity charge motion, $\overrightarrow(r)$ is the radius vector that determines the location of the charge, q is the charge value, $\left[\overrightarrow(v)\overrightarrow(r)\right]$ is the vector product.
Magnetic induction of an element with current in the SI system:
where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the element of the conductor with current (the direction is given by the direction of the current), $\vartheta$ is the angle between $ \overrightarrow(dl)$ and $\overrightarrow(r)$. The direction of the vector $\overrightarrow(dB)$ is perpendicular to the plane containing $\overrightarrow(dl)$ and $\overrightarrow(r)$. Determined by the right screw rule.
For a magnetic field, the superposition principle holds:
\[\overrightarrow(B)=\sum((\overrightarrow(B))_i\left(3\right),)\]
where $(\overrightarrow(B))_i$ are individual fields generated by moving charges, $\overrightarrow(B)$ is the total induction of the magnetic field.
Example 1
Task: Find the ratio of the forces of the magnetic and Coulomb interaction of two electrons that move with the same speed $v$ in parallel. The distance between particles is constant.
\[\overrightarrow(F_m)=q\left[\overrightarrow(v)\overrightarrow(B)\right]\left(1.1\right).\]
The field that the second moving electron creates is:
\[\overrightarrow(B)=\frac((\mu )_0)(4\pi )\frac(q\left[\overrightarrow(v)\overrightarrow(r)\right])(r^3)\left (1.2\right).\]
Let the distance between electrons be $a=r\ (constant)$. We use the algebraic property of the vector product (the Lagrange identity ($\left[\overrightarrow(a)\left[\overrightarrow(b)\overrightarrow(c)\right]\right]=\overrightarrow(b)\left(\overrightarrow(a )\overrightarrow(c)\right)-\overrightarrow(c)\left(\overrightarrow(a)\overrightarrow(b)\right)$))
\[(\overrightarrow(F))_m=\frac((\mu )_0)(4\pi )\frac(q^2)(a^3)\left[\overrightarrow(v)\left[\overrightarrow (v)\overrightarrow(a)\right]\right]=\left(\overrightarrow(v)\left(\overrightarrow(v)\overrightarrow(a)\right)-\overrightarrow(a)\left(\overrightarrow (v)\overrightarrow(v)\right)\right)=-\frac((\mu )_0)(4\pi )\frac(q^2\overrightarrow(a)v^2)(a^3) \ ,\]
$\overrightarrow(v)\left(\overrightarrow(v)\overrightarrow(a)\right)=0$ because $\overrightarrow(v\bot )\overrightarrow(a)$.
Force modulus $F_m=\frac((\mu )_0)(4\pi )\frac(q^2v^2)(a^2),\ $q=q_e=1.6\cdot 10^( -19)Cl$.
The modulus of the Coulomb force that acts on an electron in the field is equal to:
Let's find the ratio of forces $\frac(F_m)(F_q)$:
\[\frac(F_m)(F_q)=\frac((\mu )_0)(4\pi )\frac(q^2v^2)(a^2):\frac(q^2)((4 \pi (\varepsilon )_0a)^2)=(\mu )_0((\varepsilon )_0v)^2.\]
Answer: $\frac(F_m)(F_q)=(\mu )_0((\varepsilon )_0v)^2.$
Example 2
Task: A direct current of force I circulates along a coil with current in the form of a circle of radius R. Find the magnetic induction at the center of the circle.
We select an elementary section on a current-carrying conductor (Fig. 1), as a basis for solving the problem, we use the formula for the induction of a coil element with current:
where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the element of the conductor with current (the direction is given by the direction of the current), $\vartheta$ is the angle between $ \overrightarrow(dl)$ and $\overrightarrow(r)$. Based on Fig. 1 $\vartheta=90()^\circ $, therefore (2.1) will be simplified, in addition, the distance from the center of the circle (the point where we are looking for the magnetic field) of the conductor element with current is constant and equal to the radius of the coil (R), therefore we have:
All current elements will generate magnetic fields that are directed along the x axis. This means that the resulting magnetic field induction vector can be found as the sum of the projections of individual vectors $\ \ \overrightarrow(dB).$ Then, according to the superposition principle, the total magnetic field induction can be obtained by going to the integral:
Substituting (2.2) into (2.3), we get:
Answer: $B$=$\frac((\mu )_0)(2)\frac(I)(R).$
Let's understand together what a magnetic field is. After all, many people live in this field all their lives and do not even think about it. Time to fix it!
A magnetic field
A magnetic field is a special kind of matter. It manifests itself in the action on moving electric charges and bodies that have their own magnetic moment (permanent magnets).
Important: a magnetic field does not act on stationary charges! A magnetic field is also created by moving electric charges, or by a time-varying electric field, or by the magnetic moments of electrons in atoms. That is, any wire through which current flows also becomes a magnet!
A body that has its own magnetic field.
A magnet has poles called north and south. The designations "northern" and "southern" are given only for convenience (as "plus" and "minus" in electricity).
The magnetic field is represented by force magnetic lines. The lines of force are continuous and closed, and their direction always coincides with the direction of the field forces. If metal shavings are scattered around a permanent magnet, the metal particles will show a clear picture of magnetic field lines emerging from the north and entering the south pole. Graphical characteristic of the magnetic field - lines of force.
Magnetic field characteristics
The main characteristics of the magnetic field are magnetic induction, magnetic flux And magnetic permeability. But let's talk about everything in order.
Immediately, we note that all units of measurement are given in the system SI.
Magnetic induction B - vector physical quantity, which is the main power characteristic of the magnetic field. Denoted by letter B . The unit of measurement of magnetic induction - Tesla (Tl).
Magnetic induction indicates how strong a field is by determining the force with which it acts on a charge. This force is called Lorentz force.
Here q - charge, v - its speed in a magnetic field, B - induction, F is the Lorentz force with which the field acts on the charge.
F- a physical quantity equal to the product of magnetic induction by the area of the contour and the cosine between the induction vector and the normal to the plane of the contour through which the flow passes. Magnetic flux is a scalar characteristic of a magnetic field.
We can say that the magnetic flux characterizes the number of magnetic induction lines penetrating a unit area. The magnetic flux is measured in Weberach (Wb).
Magnetic permeability is the coefficient that determines the magnetic properties of the medium. One of the parameters on which the magnetic induction of the field depends is the magnetic permeability.
Our planet has been a huge magnet for several billion years. The induction of the Earth's magnetic field varies depending on the coordinates. At the equator, it is about 3.1 times 10 to the minus fifth power of Tesla. In addition, there are magnetic anomalies, where the value and direction of the field differ significantly from neighboring areas. One of the largest magnetic anomalies on the planet - Kursk And Brazilian magnetic anomaly.
The origin of the Earth's magnetic field is still a mystery to scientists. It is assumed that the source of the field is the liquid metal core of the Earth. The core is moving, which means that the molten iron-nickel alloy is moving, and the movement of charged particles is the electric current that generates the magnetic field. The problem is that this theory geodynamo) does not explain how the field is kept stable.
The earth is a huge magnetic dipole. The magnetic poles do not coincide with the geographic ones, although they are in close proximity. Moreover, the Earth's magnetic poles are moving. Their displacement has been recorded since 1885. For example, over the past hundred years, the magnetic pole in the Southern Hemisphere has shifted by almost 900 kilometers and is now in the Southern Ocean. The pole of the Arctic hemisphere is moving across the Arctic Ocean towards the East Siberian magnetic anomaly, the speed of its movement (according to 2004 data) was about 60 kilometers per year. Now there is an acceleration of the movement of the poles - on average, the speed is growing by 3 kilometers per year.
What is the significance of the Earth's magnetic field for us? First of all, the Earth's magnetic field protects the planet from cosmic rays and the solar wind. Charged particles from deep space do not fall directly to the ground, but are deflected by a giant magnet and move along its lines of force. Thus, all living things are protected from harmful radiation.
During the history of the Earth, there have been several inversions(changes) of magnetic poles. Pole inversion is when they change places. The last time this phenomenon occurred about 800 thousand years ago, and there were more than 400 geomagnetic reversals in the history of the Earth. Some scientists believe that, given the observed acceleration of the movement of the magnetic poles, the next pole reversal should be expected in the next couple of thousand years.
Fortunately, no reversal of poles is expected in our century. So, you can think about the pleasant and enjoy life in the good old constant field of the Earth, having considered the main properties and characteristics of the magnetic field. And so that you can do this, there are our authors, who can be entrusted with some of the educational troubles with confidence in success! and other types of work you can order at the link.
Magnetic field and its characteristics
Lecture plan:
Magnetic field, its properties and characteristics.
A magnetic field- the form of existence of matter surrounding moving electric charges (conductors with current, permanent magnets).
This name is due to the fact that, as the Danish physicist Hans Oersted discovered in 1820, it has an orienting effect on the magnetic needle. Oersted's experiment: a magnetic needle was placed under a wire with current, rotating on a needle. When the current was turned on, it was installed perpendicular to the wire; when changing the direction of the current, it turned in the opposite direction.
The main properties of the magnetic field:
generated by moving electric charges, conductors with current, permanent magnets and an alternating electric field;
acts with force on moving electric charges, conductors with current, magnetized bodies;
an alternating magnetic field generates an alternating electric field.
It follows from Oersted's experience that the magnetic field is directional and must have a vector force characteristic. It is designated and called magnetic induction.
The magnetic field is depicted graphically using magnetic lines of force or lines of magnetic induction. magnetic force lines are called lines along which iron filings or axes of small magnetic arrows are located in a magnetic field. At each point of such a line, the vector is directed tangentially.
The lines of magnetic induction are always closed, which indicates the absence of magnetic charges in nature and the vortex nature of the magnetic field.
Conventionally, they leave the north pole of the magnet and enter the south. The density of the lines is chosen so that the number of lines per unit area perpendicular to the magnetic field is proportional to the magnitude of the magnetic induction.
H 
Magnetic solenoid with current
The direction of the lines is determined by the rule of the right screw. Solenoid - a coil with current, the turns of which are located close to each other, and the diameter of the turn is much less than the length of the coil.
The magnetic field inside the solenoid is uniform. A magnetic field is called homogeneous if the vector is constant at any point.
The magnetic field of a solenoid is similar to the magnetic field of a bar magnet.
WITH 
The olenoid with current is an electromagnet.
Experience shows that for a magnetic field, as well as for an electric field, superposition principle: the induction of the magnetic field created by several currents or moving charges is equal to the vector sum of the inductions of the magnetic fields created by each current or charge:
The vector is entered in one of 3 ways:
a) from Ampère's law;
b) by the action of a magnetic field on a loop with current;
c) from the expression for the Lorentz force.
A 
mper experimentally established that the force with which the magnetic field acts on the element of the conductor with current I, located in a magnetic field, is directly proportional to the force
current I and the vector product of the length element and the magnetic induction:
- Ampère's law
H 
The direction of the vector can be found according to the general rules of the vector product, from which the rule of the left hand follows: if the palm of the left hand is positioned so that the magnetic lines of force enter it, and 4 outstretched fingers are directed along the current, then the bent thumb will show the direction of the force.
The force acting on a wire of finite length can be found by integrating over the entire length.
For I = const, B=const, F = BIlsin
If =90 0 , F = BIl
Magnetic field induction- a vector physical quantity numerically equal to the force acting in a uniform magnetic field on a conductor of unit length with unit current, located perpendicular to the magnetic field lines.
1Tl - induction of a uniform magnetic field, in which a 1m long conductor with a current of 1A, located perpendicular to the magnetic field lines, is acted upon by a force of 1N.
So far, we have considered macrocurrents flowing in conductors. However, according to Ampere's assumption, in any body there are microscopic currents due to the movement of electrons in atoms. These microscopic molecular currents create their own magnetic field and can turn in the fields of macrocurrents, creating an additional magnetic field in the body. The vector characterizes the resulting magnetic field created by all macro- and microcurrents, i.e. for the same macrocurrent, the vector in different media has different values.
The magnetic field of macrocurrents is described by the magnetic intensity vector .
For a homogeneous isotropic medium
0 \u003d 410 -7 H / m - magnetic constant, 0 \u003d 410 -7 N / A 2,
- magnetic permeability of the medium, showing how many times the magnetic field of macrocurrents changes due to the field of microcurrents of the medium.
magnetic flux. Gauss' theorem for magnetic flux.
vector flow(magnetic flux) through the pad dS is called a scalar value equal to
where is the projection onto the direction of the normal to the site;
- angle between vectors and .
directional surface element,
The vector flux is an algebraic quantity,
If 
- when leaving the surface;
If 
- at the entrance to the surface.
The flux of the magnetic induction vector through an arbitrary surface S is equal to
For a uniform magnetic field =const,
1 Wb - magnetic flux passing through a flat surface of 1 m 2 located perpendicular to a uniform magnetic field, the induction of which is equal to 1 T.
The magnetic flux through the surface S is numerically equal to the number of magnetic lines of force crossing the given surface.
Since the lines of magnetic induction are always closed, for a closed surface the number of lines entering the surface (Ф 0), therefore, the total flux of magnetic induction through a closed surface is zero.
- Gauss theorem: the flux of the magnetic induction vector through any closed surface is zero.
This theorem is a mathematical expression of the fact that in nature there are no magnetic charges on which the lines of magnetic induction would begin or end.
Biot-Savart-Laplace law and its application to the calculation of magnetic fields.
The magnetic field of direct currents of various shapes was studied in detail by fr. scientists Biot and Savart. They found that in all cases the magnetic induction at an arbitrary point is proportional to the strength of the current, depends on the shape, dimensions of the conductor, the location of this point in relation to the conductor and on the medium.
The results of these experiments were summarized by fr. mathematician Laplace, who took into account the vector nature of magnetic induction and hypothesized that the induction at each point is, according to the principle of superposition, the vector sum of the inductions of the elementary magnetic fields created by each section of this conductor.
Laplace in 1820 formulated a law, which was called the Biot-Savart-Laplace law: each element of a conductor with current creates a magnetic field, the induction vector of which at some arbitrary point K is determined by the formula:
- Biot-Savart-Laplace law.
It follows from the Biot-Sovar-Laplace law that the direction of the vector coincides with the direction of the cross product. The same direction is given by the rule of the right screw (gimlet).
Given that ,
Conductor element co-directional with current;
Radius vector connecting with point K;
The Biot-Savart-Laplace law is of practical importance, because allows you to find at a given point in space the induction of the magnetic field of the current flowing through the conductor of finite size and arbitrary shape.
For an arbitrary current, such a calculation is a complex mathematical problem. However, if the current distribution has a certain symmetry, then the application of the superposition principle together with the Biot-Savart-Laplace law makes it possible to calculate specific magnetic fields relatively simply.
Let's look at some examples.
A. Magnetic field of a rectilinear conductor with current.
for a conductor of finite length:
for a conductor of infinite length: 1 = 0, 2 =
B. Magnetic field at the center of the circular current:
=90 0 , sin=1,
Oersted in 1820 experimentally found that the circulation in a closed circuit surrounding a system of macrocurrents is proportional to the algebraic sum of these currents. The coefficient of proportionality depends on the choice of the system of units and in SI is equal to 1.
C 
the circulation of a vector is called a closed-loop integral.
This formula is called circulation theorem or total current law:
the circulation of the magnetic field strength vector along an arbitrary closed circuit is equal to the algebraic sum of the macrocurrents (or total current) covered by this circuit. his characteristics In the space surrounding currents and permanent magnets, there is a force field called magnetic. Availability magnetic fields shows up...
On the real structure of the electromagnetic fields And his characteristics propagation in the form of plane waves.
Article >> PhysicsON THE REAL STRUCTURE OF ELECTROMAGNETIC FIELDS AND HIS CHARACTERISTICS PROPAGATIONS IN THE FORM OF PLANE WAVES ... other components of a single fields: electromagnetic field with vector components and, electric field with components and magnetic field with components...
Magnetic field, circuits and induction
Abstract >> Physics... fields). Basic characteristic magnetic fields is his vector force magnetic induction (induction vector magnetic fields). in SI magnetic... with magnetic moment. Magnetic field And his parameters Direction magnetic lines and...
Magnetic field (2)
Abstract >> PhysicsSection of conductor AB with current in magnetic field perpendicular his magnetic lines. When shown in the figure ... the value depends only on magnetic fields and can serve his quantitative characteristic. This value is taken...
Magnetic materials (2)
Abstract >> EconomicsMaterials that interact with magnetic field expressed in his change, as well as in others ... and after the cessation of exposure magnetic fields.1. Main characteristics magnetic materialsThe magnetic properties of materials are characterized by...
A magnetic field- this is a material medium through which the interaction between conductors with current or moving charges is carried out.
Magnetic field properties:
Magnetic field characteristics:
To study the magnetic field, a test circuit with current is used. It is small, and the current in it is much less than the current in the conductor that creates the magnetic field. On opposite sides of the circuit with current from the side of the magnetic field, forces act that are equal in magnitude, but directed in opposite directions, since the direction of the force depends on the direction of the current. The points of application of these forces do not lie on one straight line. Such forces are called a couple of forces. As a result of the action of a pair of forces, the contour cannot move forward, it rotates around its axis. The rotating action is characterized torque.
, Where l–arm of a pair of forces(distance between points of application of forces).
With an increase in current in a test circuit or circuit area, the moment of a pair of forces will increase proportionally. The ratio of the maximum moment of forces acting on the current-carrying circuit to the magnitude of the current in the circuit and the area of the circuit is a constant value for a given point of the field. It's called magnetic induction.
, Where 
-magnetic moment circuits with current.
Unit magnetic induction - Tesla [T].
Magnetic moment of the circuit- vector quantity, the direction of which depends on the direction of the current in the circuit and is determined by right screw rule: clench your right hand into a fist, point four fingers in the direction of the current in the circuit, then the thumb will indicate the direction of the magnetic moment vector. The magnetic moment vector is always perpendicular to the contour plane.
Behind direction of magnetic induction vector take the direction of the vector of the magnetic moment of the circuit oriented in the magnetic field.
Line of magnetic induction- a line, the tangent to which at each point coincides with the direction of the magnetic induction vector. The lines of magnetic induction are always closed, never intersect. Lines of magnetic induction of a straight conductor with current have the form of circles located in a plane perpendicular to the conductor. The direction of the lines of magnetic induction is determined by the rule of the right screw. Lines of magnetic induction of circular current(coil with current) also have the form of circles. Each coil element is long 
can be thought of as a straight conductor that creates its own magnetic field. For magnetic fields, the principle of superposition (independent addition) is fulfilled. The total vector of the magnetic induction of the circular current is determined as the result of the addition of these fields in the center of the coil according to the rule of the right screw.
If the magnitude and direction of the magnetic induction vector are the same at each point in space, then the magnetic field is called homogeneous. If the magnitude and direction of the magnetic induction vector at each point do not change over time, then such a field is called permanent.
Value magnetic induction at any point of the field is directly proportional to the current strength in the conductor that creates the field, is inversely proportional to the distance from the conductor to a given point in the field, depends on the properties of the medium and the shape of the conductor that creates the field.
, Where 
ON 2 ; H/m is the vacuum magnetic constant,
-relative magnetic permeability of the medium,
-absolute magnetic permeability of the medium.
Depending on the magnitude of the magnetic permeability, all substances are divided into three classes:
With an increase in the absolute permeability of the medium, the magnetic induction at a given point of the field also increases. The ratio of magnetic induction to the absolute magnetic permeability of the medium is a constant value for a given point of the poly, e is called tension.
.
The vectors of tension and magnetic induction coincide in direction. The strength of the magnetic field does not depend on the properties of the medium.
Amp power- the force with which the magnetic field acts on a conductor with current.
Where l- the length of the conductor, 
- the angle between the vector of magnetic induction and the direction of the current.
The direction of the Ampere force is determined by left hand rule: the left hand is positioned so that the component of the magnetic induction vector, perpendicular to the conductor, enters the palm, direct four outstretched fingers along the current, then the thumb bent by 90 0 will indicate the direction of the Ampere force.
The result of the action of the Ampere force is the movement of the conductor in a given direction.
E 
if 
= 90 0 , then F=max, if 
= 0 0 , then F= 0.
Lorentz force- the force of the magnetic field on the moving charge.
, where q is the charge, v is the speed of its movement, 
- the angle between the vectors of tension and velocity.
The Lorentz force is always perpendicular to the magnetic induction and velocity vectors. The direction is determined by left hand rule(fingers - on the movement of a positive charge). If the direction of particle velocity is perpendicular to the lines of magnetic induction of a uniform magnetic field, then the particle moves in a circle without changing the kinetic energy.
Since the direction of the Lorentz force depends on the sign of the charge, it is used to separate charges.
magnetic flux- a value equal to the number of lines of magnetic induction that pass through any area located perpendicular to the lines of magnetic induction.
, Where 
- the angle between the magnetic induction and the normal (perpendicular) to the area S.
Unit– Weber [Wb].
Methods for measuring magnetic flux:
Changing the orientation of the site in a magnetic field (changing the angle)
Change in the area of a contour placed in a magnetic field
Changing the strength of the current that creates the magnetic field
Changing the distance of the contour from the source of the magnetic field
Change in the magnetic properties of the medium.
F 
Araday recorded an electric current in a circuit that did not contain a source, but was located next to another circuit containing a source. Moreover, the current in the primary circuit arose in the following cases: with any change in the current in circuit A, with relative movement of the circuits, with the introduction of an iron rod into circuit A, with movement of a permanent magnet relative to circuit B. The directed movement of free charges (current) occurs only in an electric field. This means that a changing magnetic field generates an electric field, which sets the free charges of the conductor in motion. This electric field is called induced or eddy.
Differences between a vortex electric field and an electrostatic one:
The source of the vortex field is a changing magnetic field.
The lines of the vortex field strength are closed.
The work done by this field to move the charge along a closed circuit is not equal to zero.
The energy characteristic of the vortex field is not the potential, but EMF induction- a value equal to the work of external forces (forces of non-electrostatic origin) in moving a unit of charge along a closed circuit.
.Measured in Volts[IN].
A vortex electric field arises with any change in the magnetic field, regardless of whether there is a conducting closed loop or not. The contour only allows to detect the vortex electric field.
Electromagnetic induction- this is the occurrence of an EMF of induction in a closed circuit with any change in the magnetic flux through its surface.
EMF of induction in a closed circuit generates an inductive current.
.
Direction of induction current determined by Lenz's rule: the induction current has such a direction that the magnetic field created by it opposes any change in the magnetic flux that generated this current.
Faraday's law for electromagnetic induction: EMF of induction in a closed loop is directly proportional to the rate of change of the magnetic flux through the surface bounded by the loop.
T 
okie foucault- eddy induction currents that occur in large conductors placed in a changing magnetic field. The resistance of such a conductor is small, since it has a large cross section S, so the Foucault currents can be large in magnitude, as a result of which the conductor heats up.
self induction- this is the occurrence of an EMF of induction in a conductor when the current strength in it changes.
A current-carrying conductor creates a magnetic field. Magnetic induction depends on the strength of the current, therefore, the own magnetic flux also depends on the strength of the current.
, where L is the coefficient of proportionality, inductance.
Unit inductance - Henry [H].
Inductance conductor depends on its size, shape and magnetic permeability of the medium.
Inductance increases with the length of the conductor, the inductance of the coil is greater than the inductance of a straight conductor of the same length, the inductance of the coil (a conductor with a large number of turns) is greater than the inductance of one turn, the inductance of the coil increases if an iron rod is inserted into it.
Faraday's law for self-induction:
.
EMF self-induction directly proportional to the rate of change of current.
EMF self-induction generates a self-induction current, which always prevents any change in the current in the circuit, that is, if the current increases, the self-induction current is directed in the opposite direction, when the current in the circuit decreases, the self-induction current is directed in the same direction. The greater the inductance of the coil, the more self-inductance EMF occurs in it.
Magnetic field energy is equal to the work that the current does to overcome the self-induction EMF during the time until the current increases from zero to a maximum value.
.
Electromagnetic vibrations- these are periodic changes in charge, current strength and all characteristics of electric and magnetic fields.
Electric oscillatory system(oscillatory circuit) consists of a capacitor and an inductor.
Conditions for the occurrence of vibrations:
The system must be brought out of equilibrium; for this, a charge is imparted to the capacitor. The energy of the electric field of a charged capacitor:
.
The system must return to a state of equilibrium. Under the influence of an electric field, the charge passes from one plate of the capacitor to another, that is, an electric current arises in the circuit, which flows through the coil. With an increase in current in the inductor, an EMF of self-induction arises, the self-induction current is directed in the opposite direction. When the current in the coil decreases, the self-induction current is directed in the same direction. Thus, the self-induction current tends to return the system to a state of equilibrium.
The electrical resistance of the circuit must be small.
Ideal oscillatory circuit has no resistance. The oscillations in it are called free.
For any electrical circuit, Ohm's law is fulfilled, according to which the EMF acting in the circuit is equal to the sum of the voltages in all sections of the circuit. There is no current source in the oscillatory circuit, but self-induction EMF arises in the inductor, which is equal to the voltage across the capacitor.
Conclusion: the charge of the capacitor changes according to the harmonic law.
Capacitor voltage:
.
Loop current:
.
Value 
- the amplitude of the current strength.
The difference from the charge on 
.
The period of free oscillations in the circuit:
Capacitor electric field energy:
Coil magnetic field energy:
The energies of the electric and magnetic fields change according to a harmonic law, but the phases of their oscillations are different: when the energy of the electric field is maximum, the energy of the magnetic field is zero.
Total energy of the oscillatory system:
.
IN ideal contour the total energy does not change.
In the process of oscillations, the energy of the electric field is completely converted into the energy of the magnetic field and vice versa. This means that the energy at any moment of time is equal to either the maximum energy of the electric field, or the maximum energy of the magnetic field.
Real oscillatory circuit contains resistance. The oscillations in it are called fading.
Ohm's law takes the form:
Provided that the damping is small (the square of the natural oscillation frequency is much greater than the square of the damping coefficient), the logarithmic damping decrement:
With strong damping (the square of the natural oscillation frequency is less than the square of the oscillation coefficient):
This equation describes the process of discharging a capacitor across a resistor. In the absence of inductance, oscillations will not occur. According to this law, the voltage across the capacitor plates also changes.
total energy in a real circuit, it decreases, since heat is released on the resistance R when current passes.
transition process- a process that occurs in electrical circuits during the transition from one mode of operation to another. Estimated time ( 
), during which the parameter characterizing the transient process will change in e times.
For circuit with capacitor and resistor:
.
Maxwell's theory of the electromagnetic field:
1 position:
Any alternating electric field generates a vortex magnetic field. An alternating electric field was called by Maxwell a displacement current, since it, like an ordinary current, induces a magnetic field.
To detect the displacement current, the passage of current through the system, which includes a capacitor with a dielectric, is considered.
Bias current density:
. The current density is directed in the direction of the change in intensity.
Maxwell's first equation:
- the vortex magnetic field is generated both by conduction currents (moving electric charges) and displacement currents (alternating electric field E).
2 position:
Any alternating magnetic field generates a vortex electric field - the basic law of electromagnetic induction.
Maxwell's second equation:
- relates the rate of change of the magnetic flux through any surface and the circulation of the vector of the electric field strength that arises in this case.
Any conductor with current creates a magnetic field in space. If the current is constant (does not change over time), then the associated magnetic field is also constant. The changing current creates a changing magnetic field. There is an electric field inside a current-carrying conductor. Therefore, a changing electric field creates a changing magnetic field.
The magnetic field is vortex, since the lines of magnetic induction are always closed. The magnitude of the magnetic field strength H is proportional to the rate of change of the electric field strength 
. Direction of the magnetic field vector 
associated with a change in the electric field strength 
by the rule of the right screw: clench the right hand into a fist, point the thumb in the direction of the change in the electric field strength, then the bent 4 fingers will indicate the direction of the lines of the magnetic field strength.
Any changing magnetic field creates a vortex electric field, whose strength lines are closed and located in a plane perpendicular to the magnetic field strength.
The magnitude of the intensity E of the vortex electric field depends on the rate of change of the magnetic field 
. The direction of the vector E is related to the direction of the change in the magnetic field H by the rule of the left screw: clench the left hand into a fist, point the thumb in the direction of the change in the magnetic field, bent four fingers will indicate the direction of the lines of the vortex electric field.
The set of vortex electric and magnetic fields connected with each other represent electromagnetic field. The electromagnetic field does not remain in the place of origin, but propagates in space in the form of a transverse electromagnetic wave.
electromagnetic wave- this is the distribution in space of vortex electric and magnetic fields connected with each other.
The condition for the occurrence of an electromagnetic wave- movement of the charge with acceleration.
Electromagnetic wave equation:
- cyclic frequency of electromagnetic oscillations
t is the time from the start of oscillations
l is the distance from the wave source to a given point in space
- wave propagation speed
The time it takes a wave to travel from a source to a given point.
The vectors E and H in an electromagnetic wave are perpendicular to each other and to the speed of wave propagation.
Source of electromagnetic waves- conductors through which fast-alternating currents (macro-emitters), as well as excited atoms and molecules (micro-emitters) flow. The higher the oscillation frequency, the better the electromagnetic waves are emitted in space.
Properties of electromagnetic waves:
All electromagnetic waves transverse
In a homogeneous medium, electromagnetic waves propagate at a constant speed, which depends on the properties of the environment:
- relative permittivity of the medium
is the vacuum dielectric constant, 
F/m, Cl 2 /nm 2
- relative magnetic permeability of the medium
- vacuum magnetic constant, 
ON 2 ; H/m
Electromagnetic waves reflected from obstacles, absorbed, scattered, refracted, polarized, diffracted, interfered.
Volumetric energy density electromagnetic field consists of volumetric energy densities of electric and magnetic fields:
Wave energy flux density - wave intensity:
-Umov-Poynting vector.
All electromagnetic waves are arranged in a series of frequencies or wavelengths ( 
). This row is electromagnetic wave scale.
Low frequency vibrations. 0 - 10 4 Hz. Obtained from generators. They don't radiate well.
radio waves. 10 4 - 10 13 Hz. Radiated by solid conductors, through which fast-alternating currents pass.
Infrared radiation- waves emitted by all bodies at temperatures above 0 K, due to intra-atomic and intra-molecular processes.
visible light- waves that act on the eye, causing a visual sensation. 380-760 nm
Ultraviolet radiation. 10 - 380 nm. Visible light and UV arise when the motion of electrons in the outer shells of an atom changes.
x-ray radiation. 80 - 10 -5 nm. Occurs when the motion of electrons in the inner shells of an atom changes.
Gamma radiation. Occurs during the decay of atomic nuclei.
Magnetic field and its characteristics. When an electric current passes through a conductor, a a magnetic field. A magnetic field is one of the types of matter. It has energy, which manifests itself in the form of electromagnetic forces acting on individual moving electric charges (electrons and ions) and on their flows, i.e. electric current. Under the influence of electromagnetic forces, moving charged particles deviate from their original path in a direction perpendicular to the field (Fig. 34). The magnetic field is formed only around moving electric charges, and its action also extends only to moving charges. Magnetic and electric fields are inseparable and form together a single electromagnetic field. Any change electric field leads to the appearance of a magnetic field and, conversely, any change in the magnetic field is accompanied by the appearance of an electric field. Electromagnetic field propagates at the speed of light, i.e. 300,000 km/s.
Graphical representation of the magnetic field. Graphically, the magnetic field is represented by magnetic lines of force, which are drawn so that the direction of the line of force at each point of the field coincides with the direction of the field forces; magnetic field lines are always continuous and closed. The direction of the magnetic field at each point can be determined using a magnetic needle. The north pole of the arrow is always set in the direction of the field forces. The end of the permanent magnet, from which the lines of force come out (Fig. 35, a), is considered to be the north pole, and the opposite end, which includes the lines of force, is the south pole (the lines of force passing inside the magnet are not shown). The distribution of lines of force between the poles of a flat magnet can be detected using steel filings sprinkled on a sheet of paper placed on the poles (Fig. 35, b). The magnetic field in the air gap between two parallel opposite poles of a permanent magnet is characterized by a uniform distribution of magnetic lines of force (Fig. 36) (field lines passing inside the magnet are not shown).
Rice. 37. Magnetic flux penetrating the coil at perpendicular (a) and inclined (b) its positions with respect to the direction of magnetic lines of force.
For a more visual representation of the magnetic field, the lines of force are located less often or thicker. In those places where the magnetic role is stronger, the lines of force are located closer to each other, in the same place where it is weaker, further apart. The lines of force do not intersect anywhere.
In many cases, it is convenient to consider magnetic lines of force as some elastic stretched threads that tend to contract and also mutually repel each other (have mutual lateral expansion). Such a mechanical representation of the lines of force makes it possible to clearly explain the emergence of electromagnetic forces during the interaction of a magnetic field and a conductor with a current, as well as two magnetic fields.
The main characteristics of a magnetic field are magnetic induction, magnetic flux, magnetic permeability and magnetic field strength.
Magnetic induction and magnetic flux. The intensity of the magnetic field, i.e., its ability to do work, is determined by a quantity called magnetic induction. The stronger the magnetic field created by a permanent magnet or electromagnet, the greater the induction it has. Magnetic induction B can be characterized by the density of magnetic lines of force, i.e., the number of lines of force passing through an area of 1 m 2 or 1 cm 2 located perpendicular to the magnetic field. Distinguish between homogeneous and inhomogeneous magnetic fields. In a uniform magnetic field, the magnetic induction at each point of the field has the same value and direction. The field in the air gap between the opposite poles of a magnet or electromagnet (see Fig. 36) can be considered homogeneous at some distance from its edges. The magnetic flux Ф passing through any surface is determined by the total number of magnetic lines of force penetrating this surface, for example, coil 1 (Fig. 37, a), therefore, in a uniform magnetic field
F = BS (40)
where S is the cross-sectional area of the surface through which the magnetic lines of force pass. It follows that in such a field the magnetic induction is equal to the flux divided by the cross-sectional area S:
B = F/S (41)
If any surface is inclined with respect to the direction of the magnetic field lines (Fig. 37, b), then the flux penetrating it will be less than when it is perpendicular, i.e. Ф 2 will be less than Ф 1.
In the SI system of units, magnetic flux is measured in webers (Wb), this unit has the dimension V * s (volt-second). Magnetic induction in the SI system of units is measured in teslas (T); 1 T \u003d 1 Wb / m 2.
Magnetic permeability. Magnetic induction depends not only on the strength of the current passing through a straight conductor or coil, but also on the properties of the medium in which the magnetic field is created. The quantity characterizing the magnetic properties of the medium is the absolute magnetic permeability? A. Its unit is the henry per meter (1 H/m = 1 Ohm*s/m).
In a medium with greater magnetic permeability, an electric current of a certain strength creates a magnetic field with greater induction. It has been established that the magnetic permeability of air and all substances, with the exception of ferromagnetic materials (see § 18), has approximately the same value as the magnetic permeability of vacuum. The absolute magnetic permeability of vacuum is called the magnetic constant, ? o \u003d 4? * 10 -7 Gn / m. The magnetic permeability of ferromagnetic materials is thousands and even tens of thousands of times greater than the magnetic permeability of non-ferromagnetic substances. Permeability ratio? and any substance to the magnetic permeability of vacuum? o is called the relative magnetic permeability:
? = ? A /? O (42)
Magnetic field strength. The intensity And does not depend on the magnetic properties of the medium, but takes into account the influence of the current strength and the shape of the conductors on the intensity of the magnetic field at a given point in space. Magnetic induction and intensity are related by the relation
H=B/? a = b/(?? o) (43)
Consequently, in a medium with a constant magnetic permeability, the magnetic field induction is proportional to its strength.
Magnetic field strength is measured in amperes per meter (A/m) or amperes per centimeter (A/cm).
