Fundamentals of electrodynamics. electrostatics The laws of classical electrodynamics relate to

Electrodynamics… Spelling dictionary-reference book

Classical theory (non-quantum) of the behavior of the electromagnetic field, which carries out the interaction between electrical. charges (electromagnetic interaction). Classical laws macroscopic E. are formulated in Maxwell’s equations, which allow ... Physical encyclopedia

- (from the word electricity, and Greek dinamis power). Part of physics that deals with the action of electric currents. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. ELECTRODYNAMICS from the word electricity, and Greek. dynamis, strength... Dictionary of foreign words of the Russian language

Modern encyclopedia

Electrodynamics- classical, theory of non-quantum electromagnetic processes in which the main role is played by interactions between charged particles in various media and in vacuum. The formation of electrodynamics was preceded by the works of C. Coulomb, J. Biot, F. Savart, ... ... Illustrated Encyclopedic Dictionary

Classical theory of electromagnetic processes in various media and in vacuum. Covers a huge set of phenomena in which the main role is played by interactions between charged particles carried out through an electromagnetic field... Big Encyclopedic Dictionary

ELECTRODYNAMICS, in physics, the field that studies the interaction between electric and magnetic fields and charged bodies. This discipline began in the 19th century. with her theoretical works James MAXWELL, she later became part of... ... Scientific and technical encyclopedic dictionary

ELECTRODYNAMICS, electrodynamics, many others. no, female (see electricity and dynamics) (physical). Department of physics, studying the properties of electric current, electricity in motion; ant. electrostatics. Ushakov's explanatory dictionary. D.N. Ushakov. 1935 1940 ... Ushakov's Explanatory Dictionary

ELECTRODYNAMICS, and, g. (specialist.). Theory of electromagnetic processes in various media and in vacuum. Ozhegov's explanatory dictionary. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 … Ozhegov's Explanatory Dictionary

Noun, number of synonyms: 2 dynamics (18) physics (55) ASIS dictionary of synonyms. V.N. Trishin. 2013… Synonym dictionary

electrodynamics- - [A.S. Goldberg. English-Russian energy dictionary. 2006] Topics of power engineering in general EN electrodynamics ... Technical Translator's Guide

Books

• Electrodynamics, A. E. Ivanov. This textbook is self-sufficient: it presents lectures that were given for a number of years by an associate professor at the specialized educational and scientific center of MSTU. N. E. Bauman...
• Electrodynamics, Sergei Anatolyevich Ivanov. ...

DEFINITION

Electromagnetic fields and electromagnetic interactions are studied by a branch of physics called electrodynamics.

Classical electrodynamics studies and describes the properties of electromagnetic fields. Examines the laws by which electromagnetic fields interact with bodies with an electric charge.

Basic concepts of electrodynamics

The basis of the electrodynamics of a stationary medium is Maxwell's equations. Electrodynamics operates with such basic concepts as electromagnetic field, electric charge, electromagnetic potential, Poynting vector.

An electromagnetic field is a special type of matter that manifests itself when one charged body interacts with another. Often, when considering an electromagnetic field, its components are distinguished: electric field and magnetic field. An electric field creates an electric charge or an alternating magnetic field. A magnetic field arises when a charge (charged body) moves and in the presence of a time-varying electric field.

Electromagnetic potential is a physical quantity that determines the distribution of the electromagnetic field in space.

Electrodynamics is divided into: electrostatics; magnetostatics; electrodynamics of continuum; relativistic electrodynamics.

The Poynting vector (Umov-Poynting vector) is a physical quantity that is the vector of the energy flux density of the electromagnetic field. The magnitude of this vector is equal to the energy that is transferred per unit time through a unit surface area that is perpendicular to the direction of propagation of electromagnetic energy.

Electrodynamics forms the basis for the study and development of optics (as a branch of science) and the physics of radio waves. This branch of science is the foundation for radio engineering and electrical engineering.

Classical electrodynamics, when describing the properties of electromagnetic fields and the principles of their interaction, uses Maxwell’s system of equations (in integral or differential forms), supplementing it with a system of material equations, boundary and initial conditions.

Maxwell's structural equations

Maxwell's system of equations has the same meaning in electrodynamics as Newton's laws in classical mechanics. Maxwell's equations were obtained as a result of generalization of numerous experimental data. Maxwell's structural equations are distinguished, writing them in integral or differential form, and material equations that connect vectors with parameters characterizing the electrical and magnetic properties of matter.

Maxwell's structural equations in integral form (in the SI system):

where is the magnetic field strength vector; is the electric current density vector; - electric displacement vector. Equation (1) reflects the law of creation of magnetic fields. A magnetic field occurs when a charge moves (electric current) or when an electric field changes. This equation is a generalization of the Biot-Savart-Laplace law. Equation (1) is called the magnetic field circulation theorem.

where is the magnetic field induction vector; - electric field strength vector; L is a closed loop through which the electric field strength vector circulates. Another name for equation (2) is the law of electromagnetic induction. Expression (2) means that the vortex electric field is generated due to an alternating magnetic field.

where is the electric charge; - charge density. Equation (3) is called the Ostrogradsky-Gauss theorem. Electric charges are sources of electric field; there are free electric charges.

Equation (4) indicates that the magnetic field is vortex. Magnetic charges do not exist in nature.

Maxwell's structural equations in differential form (SI system):

where is the electric field strength vector; - vector of magnetic induction.

where is the magnetic field strength vector; - dielectric displacement vector; - current density vector.

where is the electric charge distribution density.

Maxwell's structural equations in differential form determine the electromagnetic field at any point in space. If charges and currents are distributed continuously in space, then the integral and differential forms of Maxwell's equations are equivalent. However, if there are discontinuity surfaces, then the integral form of writing Maxwell's equations is more general.

To achieve mathematical equivalence of the integral and differential forms of Maxwell's equations, the differential notation is supplemented with boundary conditions.

From Maxwell's equations it follows that an alternating magnetic field generates an alternating electric field and vice versa, that is, these fields are inseparable and form a single electromagnetic field. The sources of the electric field can be either electric charges or a time-varying magnetic field. Magnetic fields are excited by moving electric charges (currents) or alternating electric fields. Maxwell's equations are not symmetric with respect to electric and magnetic fields. This happens because electric charges exist, but magnetic charges do not.

Material equations

Maxwell's system of structural equations is supplemented with material equations that reflect the relationship of vectors with parameters characterizing the electrical and magnetic properties of matter.

where is the relative dielectric constant, is the relative magnetic permeability, is the specific electrical conductivity, is the electrical constant, is the magnetic constant. The medium in this case is considered isotropic, non-ferromagnetic, non-ferroelectric.

Examples of problem solving

EXAMPLE 1

FUNDAMENTALS OF ELECTRODYNAMICS. ELECTROSTATICS

FUNDAMENTALS OF ELECTRODYNAMICS

Electrodynamics- the science of the properties of the electromagnetic field.

Electromagnetic field- determined by the movement and interaction of charged particles.

Manifestation of electric/magnetic field- this is the action of electric/magnetic forces:
1) frictional forces and elastic forces in the macrocosm;
2) the action of electric/magnetic forces in the microcosm (atomic structure, coupling of atoms into molecules,
transformation of elementary particles)

Discovery of the electric/magnetic field- J. Maxwell.

ELECTROSTATICS

The branch of electrodynamics studies electrically charged bodies at rest.

Elementary particles may have email charge, then they are called charged;
- interact with each other with forces that depend on the distance between particles,
but exceed many times the forces of mutual gravity (this interaction is called
electromagnetic).

Email charge- physical value determines the intensity of electric/magnetic interactions.
There are 2 signs of electric charges: positive and negative.
Particles with like charges repel, and particles with unlike charges attract.
A proton has a positive charge, an electron has a negative charge, and a neutron is electrically neutral.

Elementary charge- a minimum charge that cannot be divided.
How can we explain the presence of electromagnetic forces in nature?
- All bodies contain charged particles.
In the normal state of the body, el. neutral (since the atom is neutral), and electric/magnetic. powers are not manifested.

Body is charged, if it has an excess of charges of any sign:
negatively charged - if there is an excess of electrons;
positively charged - if there is a lack of electrons.

Electrification of bodies- this is one of the ways to obtain charged bodies, for example, by contact).
In this case, both bodies are charged, and the charges are opposite in sign, but equal in magnitude.

Law of conservation of electric charge.

In a closed system, the algebraic sum of the charges of all particles remains unchanged.
(... but not the number of charged particles, since there are transformations of elementary particles).

Closed system

A system of particles into which charged particles do not enter from the outside and do not exit.

Coulomb's law

Basic law of electrostatics.

The force of interaction between two point fixed charged bodies in a vacuum is directly proportional
the product of the charge modules and is inversely proportional to the square of the distance between them.

When bodies are considered point bodies? - if the distance between them is many times greater than the size of the bodies.
If two bodies have electric charges, then they interact according to Coulomb's law.

Unit of electric charge
1 C is a charge passing through the cross-section of a conductor in 1 second at a current of 1 A.
1 C is a very large charge.
Elemental charge:

ELECTRIC FIELD

There is an electrical charge around, materially.
The main property of the electric field: the action with force on the electric charge introduced into it.

Electrostatic field- the field of a stationary electric charge does not change with time.

Electric field strength.- quantitative characteristics of el. fields.
is the ratio of the force with which the field acts on the introduced point charge to the magnitude of this charge.
- does not depend on the magnitude of the introduced charge, but characterizes the electric field!

Tension vector direction
coincides with the direction of the force vector acting on a positive charge, and opposite to the direction of the force acting on a negative charge.

Point charge field strength:

where q0 is the charge creating the electric field.
At any point in the field, the intensity is always directed along the straight line connecting this point and q0.

ELECTRIC CAPACITY

Characterizes the ability of two conductors to accumulate electrical charge.
- does not depend on q and U.
- depends on the geometric dimensions of the conductors, their shape, relative position, electrical properties of the medium between the conductors.

SI units: (F - farad)

CAPACITORS

Electrical device that stores charge
(two conductors separated by a dielectric layer).

Where d is much smaller than the dimensions of the conductor.

Designation on electrical diagrams:

The entire electric field is concentrated inside the capacitor.
The charge of a capacitor is the absolute value of the charge on one of the capacitor plates.

Types of capacitors:
1. by type of dielectric: air, mica, ceramic, electrolytic
2. according to the shape of the plates: flat, spherical.
3. by capacity: constant, variable (adjustable).

Electrical capacitance of a flat capacitor

where S is the area of ​​the plate (plating) of the capacitor
d - distance between plates
eo - electrical constant
e - dielectric constant of the dielectric

Including capacitors in an electrical circuit

parallel

sequential

Then the total electrical capacity (C):

when connected in parallel

.

when connected in series

DC AC CONNECTIONS

Electricity- ordered movement of charged particles (free electrons or ions).
In this case, electricity is transferred through the cross section of the conductor. charge (during the thermal movement of charged particles, the total transferred electrical charge = 0, since positive and negative charges are compensated).

Email direction current- it is conventionally accepted to consider the direction of movement of positively charged particles (from + to -).

Email actions current (in conductor):

thermal effect of current- heating of the conductor (except for superconductors);

chemical effect of current - appears only in electrolytes. Substances that make up the electrolyte are released on the electrodes;

magnetic effect of current(main) - observed in all conductors (deflection of the magnetic needle near a conductor with current and the force effect of the current on neighboring conductors through a magnetic field).

OHM'S LAW FOR A CIRCUIT SECTION

where , R is the resistance of the circuit section. (the conductor itself can also be considered a section of the circuit).

Each conductor has its own specific current-voltage characteristic.

RESISTANCE

Basic electrical characteristics of a conductor.
- according to Ohm's law, this value is constant for a given conductor.

1 Ohm is the resistance of a conductor with a potential difference at its ends
at 1 V and the current strength in it is 1 A.

Resistance depends only on the properties of the conductor:

where S is the cross-sectional area of ​​the conductor, l is the length of the conductor,
ro - resistivity characterizing the properties of the conductor substance.

ELECTRICAL CIRCUITS

They consist of a source, a consumer of electric current, wires, and a switch.

SERIES CONNECTION OF CONDUCTORS

I - current strength in the circuit
U - voltage at the ends of the circuit section

PARALLEL CONNECTION OF CONDUCTORS

I - current strength in an unbranched section of the circuit
U - voltage at the ends of the circuit section
R - total resistance of the circuit section

Remember how measuring instruments are connected:

Ammeter - connected in series with the conductor in which the current is measured.

Voltmeter - connected in parallel to the conductor on which the voltage is measured.

DC OPERATION

Current work- this is the work of the electric field to transfer electric charges along the conductor;

The work done by the current on a section of the circuit is equal to the product of the current, voltage and time during which the work was performed.

Using the formula of Ohm's law for a section of a circuit, you can write several versions of the formula for calculating the work of the current:

According to the law of conservation of energy:

The work is equal to the change in the energy of a section of the circuit, so the energy released by the conductor is equal to the work of the current.

In the SI system:

JOULE-LENZ LAW

When current passes through a conductor, the conductor heats up and heat exchange occurs with the environment, i.e. the conductor gives off heat to the bodies surrounding it.

The amount of heat released by a conductor carrying current into the environment is equal to the product of the square of the current strength, the resistance of the conductor and the time the current passes through the conductor.

According to the law of conservation of energy, the amount of heat released by a conductor is numerically equal to the work done by the current flowing through the conductor during the same time.

In the SI system:

[Q] = 1 J

DC POWER

The ratio of the work done by the current during time t to this time interval.

In the SI system:

The phenomenon of superconductivity

Discovery of low temperature superconductivity:
1911 - Dutch scientist Kamerling - Onnes
observed at ultra-low temperatures (below 25 K) in many metals and alloys;
At such temperatures, the resistivity of these substances becomes vanishingly small.

In 1957, a theoretical explanation of the phenomenon of superconductivity was given:
Cooper (USA), Bogolyubov (USSR)

1957 Collins's experiment: the current in a closed circuit without a current source did not stop for 2.5 years.

In 1986, high-temperature superconductivity (at 100 K) was discovered (for metal-ceramics).

Difficulty of achieving superconductivity:
- the need for strong cooling of the substance

Application area:
- obtaining strong magnetic fields;
- powerful electromagnets with superconducting winding in accelerators and generators.

Currently in the energy sector there is a big problem
- large losses of electricity during transmission her by wire.

Possible Solution Problems:
with superconductivity, the resistance of the conductors is approximately 0
and energy losses are sharply reduced.

Substance with the highest superconducting temperature
In 1988 in the USA, at a temperature of –148°C, the phenomenon of superconductivity was obtained. The conductor was a mixture of thallium, calcium, barium and copper oxides - Tl2Ca2Ba2Cu3Ox.

Semiconductor -

A substance whose resistivity can vary over a wide range and decreases very quickly with increasing temperature, which means that the electrical conductivity (1/R) increases.
- observed in silicon, germanium, selenium and some compounds.

Conduction mechanism in semiconductors

Semiconductor crystals have an atomic crystal lattice where outer electrons are bonded to neighboring atoms by covalent bonds.
At low temperatures, pure semiconductors have no free electrons and behave like an insulator.

ELECTRIC CURRENT IN VACUUM

What is a vacuum?
- this is the degree of rarefaction of a gas at which there are practically no collisions of molecules;

Electric current is not possible because the possible number of ionized molecules cannot provide electrical conductivity;
- it is possible to create electric current in a vacuum if you use a source of charged particles;
- the action of a source of charged particles can be based on the phenomenon of thermionic emission.

Thermionic emission

- this is the emission of electrons by solid or liquid bodies when they are heated to temperatures corresponding to the visible glow of hot metal.
The heated metal electrode continuously emits electrons, forming an electron cloud around itself.
In an equilibrium state, the number of electrons that left the electrode is equal to the number of electrons that returned to it (since the electrode becomes positively charged when electrons are lost).
The higher the temperature of the metal, the higher the density of the electron cloud.

Vacuum diode

Electric current in a vacuum is possible in vacuum tubes.
A vacuum tube is a device that uses the phenomenon of thermionic emission.

A vacuum diode is a two-electrode (A - anode and K - cathode) electron tube.
Very low pressure is created inside the glass container

H - filament placed inside the cathode to heat it. The surface of the heated cathode emits electrons. If the anode is connected to + of the current source, and the cathode is connected to -, then the circuit flows
constant thermionic current. The vacuum diode has one-way conductivity.
Those. current in the anode is possible if the anode potential is higher than the cathode potential. In this case, electrons from the electron cloud are attracted to the anode, creating an electric current in a vacuum.

Current-voltage characteristic of a vacuum diode.

At low anode voltages, not all the electrons emitted by the cathode reach the anode, and the electric current is small. At high voltages, the current reaches saturation, i.e. maximum value.
A vacuum diode is used to rectify alternating current.

Current at the input of the diode rectifier:

Rectifier output current:

Electron beams

This is a stream of rapidly flying electrons in vacuum tubes and gas-discharge devices.

Properties of electron beams:

Deflects in electric fields;
- deflect in magnetic fields under the influence of the Lorentz force;
- when a beam hitting a substance is decelerated, X-ray radiation appears;
- causes glow (luminescence) of some solids and liquids (luminophores);
- heat the substance by contacting it.

Cathode ray tube (CRT)

Thermionic emission phenomena and properties of electron beams are used.

A CRT consists of an electron gun, horizontal and vertical deflectors
electrode plates and screen.
In an electron gun, electrons emitted by a heated cathode pass through the control grid electrode and are accelerated by the anodes. An electron gun focuses an electron beam into a point and changes the brightness of the light on the screen. Deflecting horizontal and vertical plates allow you to move the electron beam on the screen to any point on the screen. The tube screen is coated with a phosphor that begins to glow when bombarded with electrons.

There are two types of tubes:

1) with electrostatic control of the electron beam (deflection of the electric beam only by the electric field);
2) with electromagnetic control (magnetic deflection coils are added).

Main applications of CRT:

picture tubes in television equipment;
computer displays;
electronic oscilloscopes in measuring technology.

ELECTRIC CURRENT IN GASES

Under normal conditions, gas is a dielectric, i.e. it consists of neutral atoms and molecules and does not contain free carriers of electric current.
The conductor gas is an ionized gas. Ionized gas has electron-ion conductivity.

Air is a dielectric in power lines, air capacitors, and contact switches.

Air is a conductor when lightning, an electric spark occurs, or when a welding arc occurs.

Gas ionization

It is the breakdown of neutral atoms or molecules into positive ions and electrons by removing electrons from the atoms. Ionization occurs when a gas is heated or exposed to radiation (UV, X-rays, radioactive) and is explained by the disintegration of atoms and molecules during collisions at high speeds.

Gas discharge

This is electric current in ionized gases.
The charge carriers are positive ions and electrons. Gas discharge is observed in gas-discharge tubes (lamps) when exposed to an electric or magnetic field.

Recombination of charged particles

- the gas ceases to be a conductor if ionization stops, this occurs as a result of recombination (reunion of oppositely charged particles).

There is a self-sustaining and non-self-sustaining gas discharge.

Non-self-sustaining gas discharge

If the action of the ionizer is stopped, the discharge will also stop.

When the discharge reaches saturation, the graph becomes horizontal. Here, the electrical conductivity of the gas is caused only by the action of the ionizer.

Self-sustaining gas discharge

In this case, the gas discharge continues even after the termination of the external ionizer due to ions and electrons resulting from impact ionization (= ionization of electric shock); occurs when the potential difference between the electrodes increases (an electron avalanche occurs).
A non-self-sustained gas discharge can transform into a self-sustained gas discharge when Ua = Uignition.

Electrical breakdown of gas

The process of transition of a non-self-sustaining gas discharge into a self-sustaining one.

Self-sustained gas discharge occurs 4 types:

1. smoldering - at low pressures (up to several mm Hg) - observed in gas-light tubes and gas lasers.
2. spark - at normal pressure and high electric field strength (lightning - current strength up to hundreds of thousands of amperes).
3. corona - at normal pressure in a non-uniform electric field (at the tip).
4. arc - high current density, low voltage between the electrodes (gas temperature in the arc channel -5000-6000 degrees Celsius); observed in spotlights and projection film equipment.

These discharges are observed:

smoldering - in fluorescent lamps;
spark - in lightning;
corona - in electric precipitators, during energy leakage;
arc - during welding, in mercury lamps.

Plasma

This is the fourth state of aggregation of a substance with a high degree of ionization due to the collision of molecules at high speed at high temperature; found in nature: ionosphere - weakly ionized plasma, Sun - fully ionized plasma; artificial plasma - in gas-discharge lamps.

Plasma can be:

Low temperature - at temperatures less than 100,000K;
high temperature - at temperatures above 100,000K.

Basic properties of plasma:

High electrical conductivity
- strong interaction with external electric and magnetic fields.

At a temperature

Any substance is in a plasma state.

Interestingly, 99% of the matter in the Universe is plasma

TEST QUESTIONS FOR TESTING

Coulomb's Law:

Where F – the force of electrostatic interaction between two charged bodies;

q 1 , q 2 – electric charges of bodies;

ε – relative dielectric constant of the medium;

ε 0 =8.85·10 -12 F/m – electrical constant;

r– the distance between two charged bodies.

Linear charge density:

where d q – elementary charge per section of length d l.

Surface charge density:

where d q – elementary charge on surface d s.

Volume charge density:

where d q – elementary charge, in volume d V.

Electric field strength:

Where F – force acting on the charge q.

Gauss's theorem:

Where E– electrostatic field strength;

d S – vector , the module of which is equal to the area of ​​the surface being penetrated, and the direction coincides with the direction of the normal to the site;

q– algebraic sum of prisoners inside the surface d S charges.

Theorem on the circulation of the tension vector:

Electrostatic field potential:

Where W p – potential energy of a point charge q.

Point charge potential:

Point charge field strength:

.

The field strength created by an infinite straight uniformly charged line or an infinitely long cylinder:

Where τ – linear charge density;

r– the distance from the thread or cylinder axis to the point at which the field strength is determined.

The field strength created by an infinite uniform charged plane:

where σ is the surface charge density.

The relationship between potential and tension in the general case:

E= – gradφ = .

Relationship between potential and intensity in the case of a uniform field:

E= ,

Where d– distance between points with potentials φ 1 and φ 2.

Relationship between potential and intensity in the case of a field with central or axial symmetry:

The work of field forces to move a charge q from a field point with potential φ 1 to a point with potential φ 2:

A=q(φ 1 – φ 2).

Electrical capacity of the conductor:

Where q– conductor charge;

φ is the potential of the conductor, provided that at infinity the potential of the conductor is taken equal to zero.

Capacitance of the capacitor:

Where q– capacitor charge;

U– potential difference between the capacitor plates.

Electrical capacity of a flat capacitor:

where ε is the dielectric constant of the dielectric located between the plates;

d– distance between plates;

S– total area of ​​the plates.

Electrical capacity of the capacitor bank:

b) with parallel connection:

Energy of a charged capacitor:

,

Where q– capacitor charge;

U– potential difference between the plates;

C– electrical capacity of the capacitor.

DC Power:

where d q– charge flowing through the cross section of the conductor during time d t.

Current Density:

Where I– current strength in the conductor;

S– conductor area.

Ohm's law for a circuit section that does not contain EMF:

Where I– current strength in the area;

U

R– resistance of the area.

Ohm's law for a section of a circuit containing an emf:

Where I– current strength in the area;

U– voltage at the ends of the section;

R– total resistance of the section;

ε – EMF of the source.

Ohm's law for a closed (complete) circuit:

Where I– current strength in the circuit;

R– external resistance of the circuit;

r– internal resistance of the source;

ε – EMF of the source.

Kirchhoff's laws:

2. ,

where is the algebraic sum of current strengths converging at a node;

– algebraic sum of voltage drops in the circuit;

– algebraic sum of the EMF in the circuit.

Conductor resistance:

Where R– conductor resistance;

ρ – conductor resistivity;

l– length of the conductor;

S

Conductor conductivity:

Where G– conductivity of the conductor;

γ – conductivity of the conductor;

l– length of the conductor;

S– cross-sectional area of ​​the conductor.

Conductor system resistance:

a) with a serial connection:

a) in parallel connection:

Current work:

,

Where A– current work;

U- voltage;

I– current strength;

R- resistance;

t- time.

Current power:

.

Joule–Lenz law

Where Q– the amount of heat released.

Ohm's law in differential form:

j=γ E ,

Where j – current density;

γ – specific conductivity;

E– electric field strength.

Relationship between magnetic induction and magnetic field strength:

B=μμ 0 H ,

Where B – magnetic induction vector;

μ– magnetic permeability;

H– magnetic field strength.

Biot-Savart-Laplace law:

,

where d B – magnetic field induction created by a conductor at a certain point;

μ – magnetic permeability;

μ 0 =4π·10 -7 H/m – magnetic constant;

I– current strength in the conductor;

d l – conductor element;

r– radius vector drawn from element d l conductor to the point at which the magnetic field induction is determined.

Total current law for magnetic field (vector circulation theorem B):

,

Where n– number of conductors with currents covered by the circuit L free form.

Magnetic induction at the center of the circular current:

Where R– radius of the circular turn.

Magnetic induction on the axis of circular current:

,

Where h– the distance from the center of the coil to the point at which the magnetic induction is determined.

Magnetic induction of forward current field:

Where r 0 – distance from the axis of the wire to the point at which magnetic induction is determined.

Magnetic induction of solenoid field:

B=μμ 0 nI,

Where n– the ratio of the number of turns of the solenoid to its length.

Ampere Power:

d F =I,

where d F – Ampere power;

I– current strength in the conductor;

d l – length of the conductor;

B– magnetic field induction.

Lorentz force:

F=q E +q[v B ],

Where F – Lorentz force;

q– particle charge;

E– electric field strength;

v– particle speed;

B– magnetic field induction.

Magnetic Flux:

a) in the case of a uniform magnetic field and a flat surface:

Φ=B n S,

Where Φ – magnetic flux;

Bn– projection of the magnetic induction vector onto the normal vector;

S– contour area;

b) in the case of a non-uniform magnetic field and arbitrary projection:

Flux linkages (full flow) for toroid and solenoid:

Where Ψ – full flow;

N – number of turns;

Φ – magnetic flux permeating one turn.

Loop Inductance:

Solenoid inductance:

L=μμ 0 n 2 V,

Where L– solenoid inductance;

μ – magnetic permeability;

μ 0 – magnetic constant;

n– the ratio of the number of turns to its length;

V– solenoid volume.

Faraday's law of electromagnetic induction:

where ε i– induced emf;

– change in total flow per unit time.

Work to move a closed loop in a magnetic field:

A=IΔ Φ,

Where A– work on moving the contour;

I– current strength in the circuit;

Δ Φ – change in the magnetic flux passing through the circuit.

Self-induced emf:

Magnetic field energy:

Volumetric magnetic field energy density:

,

where ω is the volumetric magnetic field energy density;

B– magnetic field induction;

H– magnetic field strength;

μ – magnetic permeability;

μ 0 – magnetic constant.

3.2. Concepts and definitions

? List the properties of electric charge.

1. There are two types of charges - positive and negative.

2. Like charges repel, unlike charges attract.

3. Charges have the property of discreteness - all are multiples of the smallest elementary.

4. The charge is invariant, its value does not depend on the reference system.

5. The charge is additive - the charge of a system of bodies is equal to the sum of the charges of all bodies of the system.

6. The total electric charge of a closed system is a constant value

7. A stationary charge is a source of an electric field, a moving charge is a source of a magnetic field.

? Formulate Coulomb's law.

The force of interaction between two stationary point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The force is directed along the line connecting the charges.

? What is an electric field? Electric field strength? Formulate the principle of superposition of electric field strength.

An electric field is a type of matter associated with electric charges and transmitting the action of one charge to another. Tension is a force characteristic of a field equal to the force acting on a unit positive charge placed at a given point in the field. The principle of superposition - the field strength created by a system of point charges is equal to the vector sum of the field strengths of each charge.

? What are the lines of force of an electrostatic field called? List the properties of lines of force.

A line whose tangent at each point coincides with the direction of the field strength vector is called a force line. Properties of lines of force - they begin on positive charges, end on negative charges, are not interrupted, and do not intersect each other.

? Give the definition of an electric dipole. Dipole field.

A system of two equal in magnitude, opposite in sign point electric charges, the distance between which is small compared to the distance to the points where the action of these charges is observed. The intensity vector has the direction opposite to the vector of the electric moment of the dipole (which, in turn, is directed away from negative charge to positive charge).

? What is electrostatic field potential? Formulate the principle of potential superposition.

A scalar quantity numerically equal to the ratio of the potential energy of an electric charge placed at a given point in the field to the magnitude of this charge. The principle of superposition - the potential of a system of point charges at a certain point in space is equal to the algebraic sum of the potentials that these charges would create separately at the same point in space.

? What is the relationship between tension and potential?

E=- (E is the field strength at a given point in the field, j is the potential at this point.)

? Define the concept of “electric field strength vector flow”. State Gauss's electrostatic theorem.

For an arbitrary closed surface, the flux of the tension vector E electric field F E= . Gauss's theorem:

= (here Qi– charges covered by a closed surface). Valid for a closed surface of any shape.

? What substances are called conductors? How are charges and electrostatic field distributed in a conductor? What is electrostatic induction?

Conductors are substances in which free charges can move in an orderly manner under the influence of an electric field. Under the influence of an external field, the charges are redistributed, creating their own field, equal in magnitude to the external one and directed oppositely. Therefore, the resulting voltage inside the conductor is 0.

Electrostatic induction is a type of electrification in which, under the influence of an external electric field, a redistribution of charges occurs between parts of a given body.

? What is the electrical capacity of a solitary conductor or capacitor? How to determine the capacitance of a flat capacitor, a bank of capacitors connected in series or in parallel? Unit of measurement of electrical capacity.

Solitary guide: where WITH-capacity, q- charge, j - potential. The unit of measurement is farad [F]. (1 F is the capacitance of a conductor whose potential increases by 1 V when a charge of 1 C is imparted to the conductor).

Capacitance of a parallel plate capacitor. Serial connection: . Parallel connection: C total = C 1 +C 2 +…+S n

? What substances are called dielectrics? What types of dielectrics do you know? What is polarization of dielectrics?

Dielectrics are substances in which, under normal conditions, there are no free electrical charges. There are polar, non-polar, and ferroelectric dielectrics. Polarization is the process of orientation of dipoles under the influence of an external electric field.

? What is an electrical displacement vector? Formulate Maxwell's postulate.

Electrical displacement vector D characterizes the electrostatic field created by free charges (i.e. in a vacuum), but with such a distribution in space as in the presence of a dielectric. Maxwell's postulate: . Physical meaning - expresses the law of creation of electric fields by the action of charges in arbitrary media.

? Formulate and explain the boundary conditions for the electrostatic field.

When an electric field passes through the interface between two dielectric media, the intensity vector and displacement change abruptly in magnitude and direction. The relationships characterizing these changes are called boundary conditions. There are 4 of them:

(3), (4)

? How is the energy of an electrostatic field determined? Energy density?

Energy W= ( E- field strength, e-dielectric constant, e 0 -electric constant, V- field volume), energy density

? Define the concept of “electric current”. Types of currents. Characteristics of electric current. What condition is necessary for its emergence and existence?

Current is the ordered movement of charged particles. Types - conduction current, ordered movement of free charges in a conductor, convection - occurs when a charged macroscopic body moves in space. For the emergence and existence of a current, it is necessary to have charged particles capable of moving in an orderly manner, and the presence of an electric field, the energy of which, being replenished, would be spent on this ordered movement.

? Give and explain the continuity equation. Formulate the condition for the current to be stationary in integral and differential forms.

Continuity equation. Expresses the law of conservation of charge in differential form. Condition for stationarity (constancy) of the current in integral form: and differential - .

? Write Ohm's law in integral and differential forms.

Integral form – ( I-current, U- voltage, R-resistance). Differential form - ( j - current density, g - electrical conductivity, E - field strength in the conductor).

? What are outside forces? EMF?

Outside forces separate charges into positive and negative. EMF is the ratio of the work of moving a charge along the entire closed circuit to its value

? How is work and current power determined?

When moving a charge q through an electrical circuit at the ends of which voltage is applied U, work is done by the electric field, current power (t-time)

? Formulate Kirchhoff's rules for branched chains. What conservation laws are included in Kirchhoff's rules? How many independent equations must be constructed based on Kirchhoff's first and second laws?

1. The algebraic sum of currents converging at a node is equal to 0.

2. In any arbitrarily chosen closed circuit, the algebraic sum of the voltage drops is equal to the algebraic sum of the emfs occurring in this circuit. Kirchhoff's first rule follows from the law of conservation of electric charge. The number of equations in total must be equal to the number of desired quantities (the system of equations must include all resistance and emf).

? Electric current in gas. Processes of ionization and recombination. The concept of plasma.

Electric current in gases is the directed movement of free electrons and ions. Under normal conditions, gases are dielectrics and become conductors after ionization. Ionization is the process of forming ions by separating electrons from gas molecules. Occurs due to exposure to an external ionizer - strong heating, X-ray or ultraviolet irradiation, electron bombardment. Recombination is the reverse process of ionization. Plasma is a fully or partially ionized gas in which the concentrations of positive and negative charges are equal.

? Electric current in a vacuum. Thermionic emission.

Current carriers in a vacuum are electrons emitted due to emission from the surface of the electrodes. Thermionic emission is the emission of electrons by heated metals.

? What do you know about the phenomenon of superconductivity?

A phenomenon in which the resistance of some pure metals (tin, lead, aluminum) drops to zero at temperatures close to absolute zero.

? What do you know about the electrical resistance of conductors? What is resistivity, its dependence on temperature, electrical conductivity? What do you know about series and parallel connection of conductors. What is a shunt, additional resistance?

Resistance is a value directly proportional to the length of the conductor l and inversely proportional to area S conductor cross-section: (r-resistivity). Conductivity is the reciprocal of resistance. Specific resistance (resistance of a conductor 1 m long with a cross section of 1 m2). Specific resistance depends on temperature, here a is the temperature coefficient, R And R 0 , r and r 0 – resistances and resistivities at t and 0 0 C. Parallel - , sequential R=R 1 +R 2 +…+Rn. A shunt resistor is connected in parallel with an electrical measuring instrument to divert part of the electric current to expand the measurement limits.

? A magnetic field. What sources can create a magnetic field?

A magnetic field is a special type of matter through which moving electric charges interact. The reason for the existence of a constant magnetic field is a stationary conductor with a constant electric current, or permanent magnets.

? Formulate Ampere's law. How do conductors through which current flows in one (opposite) direction interact?

A current-carrying conductor is acted upon by an Ampere force equal to .

B - magnetic induction, I- current in conductor, D l– length of the conductor section, a-angle between the magnetic induction and the conductor section. In one direction they attract, in the opposite direction they repel.

? Define Ampere force. How to determine its direction?

This is the force acting on a current-carrying conductor placed in a magnetic field. We determine the direction as follows: we position the palm of the left hand so that the magnetic induction lines enter it, and the four extended fingers are directed along the current in the conductor. The bent thumb will show the direction of the Ampere force.

? Explain the movement of charged particles in a magnetic field. What is the Lorentz force? What is its direction?

A moving charged particle creates its own magnetic field. If it is placed in an external magnetic field, then the interaction of the fields will manifest itself in the emergence of a force acting on the particle from the external field - the Lorentz force. The direction is according to the left hand rule. For a positive charge - vector B enters the palm of the left hand, four fingers are directed along the movement of the positive charge (velocity vector), the bent thumb shows the direction of the Lorentz force. On a negative charge, the same force acts in the opposite direction.

(q-charge, v-speed, B- induction, a- angle between the direction of speed and magnetic induction).

? A frame with current in a uniform magnetic field. How is magnetic moment determined?

The magnetic field has an orienting effect on the current-carrying frame, turning it in a certain way. The torque is determined by the formula: M =p m x B , Where p m- vector of the magnetic moment of the frame with current, equal to IS n (current per contour surface area, per unit normal to the contour), B -magnetic induction vector, quantitative characteristic of the magnetic field.

? What is the magnetic induction vector? How to determine its direction? How is a magnetic field graphically represented?

The magnetic induction vector is the force characteristic of the magnetic field. The magnetic field is clearly depicted using lines of force. At each point of the field, the tangent to the field line coincides with the direction of the magnetic induction vector.

? Formulate and explain the Biot–Savart–Laplace law.

The Biot-Savart-Laplace law allows you to calculate for a conductor with current I magnetic field induction d B , created at an arbitrary point in the field d l conductor: (here m 0 is the magnetic constant, m is the magnetic permeability of the medium). The direction of the induction vector is determined by the rule of the right screw if the translational movement of the screw corresponds to the direction of the current in the element.

? State the principle of superposition for a magnetic field.

The principle of superposition - the magnetic induction of the resulting field created by several currents or moving charges is equal to the vector sum of the magnetic induction of the added fields created by each current or moving charge separately:

? Explain the main characteristics of a magnetic field: magnetic flux, magnetic field circulation, magnetic induction.

Magnetic flux F through any surface S called a quantity equal to the product of the magnitude of the magnetic induction vector and the area S and the cosine of the angle a between the vectors B And n (outer normal to the surface). Vector circulation B over a given closed contour is called an integral of the form , where d l - vector of the elementary length of the contour. Vector circulation theorem B : vector circulation B along an arbitrary closed circuit is equal to the product of the magnetic constant and the algebraic sum of the currents covered by this circuit. The magnetic induction vector is the force characteristic of the magnetic field. The magnetic field is clearly depicted using lines of force. At each point of the field, the tangent to the field line coincides with the direction of the magnetic induction vector.

? Write down and comment on the condition for the magnetic field to be solenoidal in integral and differential forms.

Vector fields in which there are no sources and sinks are called solenoidal. Condition for solenoidal magnetic field in integral form: and differential form:

? Magnetics. Types of magnets. Feromagnets and their properties. What is hysteresis?

A substance is magnetic if it is capable of acquiring a magnetic moment (magnetization) under the influence of a magnetic field. Substances that are magnetized in an external magnetic field against the direction of the field are called diamagnetic substances. Substances that are magnetized in an external magnetic field in the direction of the field are called paramagnetic substances. These two classes are called weakly magnetic substances. Strongly magnetic substances that are magnetized even in the absence of an external magnetic field are called ferromagnets . Magnetic hysteresis is the difference in the magnetization values ​​of a ferromagnet at the same magnetizing field strength H depending on the value of the preliminary magnetization. This graphical dependence is called a hysteresis loop.

? Formulate and explain the law of total current in integral and differential forms (the main levels of magnetostatics in matter).

? What is electromagnetic induction? Formulate and explain the basic law of electromagnetic induction (Faraday's law). State Lenz's rule.

The phenomenon of the occurrence of electromotive force (induction emf) in a conductor located in an alternating magnetic field or moving in a constant magnetic field is called electromagnetic induction. Faraday's law: whatever the reason for the change in the flux of magnetic induction covered by a closed conducting loop, arising in the EMF loop

The minus sign is determined by Lenz's rule - the induced current in the circuit always has such a direction that the magnetic field it creates prevents the change in the magnetic flux that caused this induced current.

? What is the phenomenon of self-induction? What is inductance, units of measurement? Currents when closing and opening an electrical circuit.

The occurrence of induced emf in a conductive circuit under the influence of its own magnetic field when it changes, resulting from a change in the current strength in the conductor. Inductance is a proportionality coefficient depending on the shape and size of the conductor or circuit, [H]. In accordance with Lenz's rule, the self-inductive emf prevents the current from increasing when the circuit is turned on and the current from decreasing when the circuit is turned off. Therefore, the magnitude of the current cannot change instantly (the mechanical analogue is inertia).

? The phenomenon of mutual induction. Mutual induction coefficient.

If two stationary circuits are located close to each other, then when the current strength in one circuit changes, an emf occurs in the other circuit. This phenomenon is called mutual induction. Proportionality coefficients L 21 and L 12 is called the mutual inductance of the circuits, they are equal.

? Write Maxwell's equations in integral form. Explain their physical meaning.

; ;

; .

From Maxwell's theory it follows that the electric and magnetic fields cannot be considered as independent - a change in time of one leads to a change in the other.

? Magnetic field energy. Magnetic field energy density.

Energy, L-inductance, I– current strength.

Density , IN- magnetic induction, N– magnetic field strength, V-volume.

? The principle of relativity in electrodynamics

The general laws of electromagnetic fields are described by Maxwell's equations. In relativistic electrodynamics it has been established that the relativistic invariance of these equations occurs only under the condition of relativity of electric and magnetic fields, i.e. when the characteristics of these fields depend on the choice of inertial reference systems. In a moving system, the electric field is the same as in a stationary system, but in a moving system there is a magnetic field, which is not present in a stationary system.

Oscillations and waves