PHYSICS

The law of conservation of charge. Coulomb's law. The dielectric constant of a substance.

The law of conservation of electric charge states that the algebraic sum of the charges of an electrically closed system is conserved.

The law of conservation of charge in integral form:

Here Ω is some arbitrary region in three-dimensional space, is the boundary of this region, ρ is the charge density, is the current density (flux density of electric charge) through the boundary.

The law of conservation of charge in differential form:

The law of conservation of charge in electronics:

Kirchhoff's rules for currents follow directly from the law of conservation of charge. The combination of conductors and radio-electronic components is represented as an open system. The total influx of charges into a given system is equal to the total output of charges from the system. Kirchhoff's rules assume that an electronic system cannot significantly change its total charge.

Coulomb's law. The module of the interaction force of two point charges in vacuum is directly proportional to the product of the modules of these charges and inversely proportional to the square of the distance between them. where is the force with which charge 1 acts on charge 2; q1,q2 - magnitude of charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in modulus, to the distance between charges - r12); k - coefficient of proportionality. Thus, the law indicates that charges of the same name repel (and opposite charges attract).

The dielectric constant of a substance. The physical quantity equal to the ratio of the modulus of the external electric field in vacuum to the modulus of the total field in a homogeneous dielectric is called the permittivity of the substance.

Electric field. Electric field strength. Method of superposition of electric fields.

Electric field - one of the components of the electromagnetic field; a special kind of matter that exists around bodies or particles that have an electric charge, as well as in free form when changing magnetic field(for example, in electromagnetic waves). The electric field is directly invisible, but can be observed due to its force effect on charged bodies.

Electric field strength - vector physical quantity characterizing the electric field at a given point and numerically equal to the ratio of the force acting on the test charge placed at a given point of the field to the value of this charge q: .

Method of superposition of electric fields. If the field is formed not by one charge, but by several, then the forces acting on the test charge are added according to the vector addition rule. Therefore, the intensity of the system of charges at a given point, the field is equal to the vector sum of the field strengths from each charge separately.

The flow of the electric field strength vector. electrical displacement. Ostrogradsky-Gauss theorem.

electric field strength across a given surface

the sum of flows through all areas into which the surface is divided

electrical displacement. Due to the different polarizability of dissimilar dielectrics, the field strengths in them will be different. Therefore, the number of lines of force in each dielectric is also different.

Part of the lines emanating from charges surrounded by a closed surface will end at the dielectric interface and will not penetrate this surface. This difficulty can be eliminated by introducing into consideration a new physical characteristic of the field - the electric displacement vector

The vector is directed in the same direction as. The concept of vector lines and displacement flux, similar to the concept of force lines and intensity flux dN0= DdScos(α)

Ostrogradsky's formula - a formula that expresses the flow of a vector field through a closed surface by the integral of the divergence (how far the incoming and outgoing flows diverge) of this field over the volume bounded by this surface: that is, the integral of the divergence of the vector field , distributed over some volume T, is equal to the vector flow through the surface S that bounds this volume.

Application of the Gauss theorem to the calculation of some electric fields in vacuum.

a) The field of an infinitely long thread

the modulus of the field strength created by a uniformly charged infinitely long filament at a distance R from it,

b) the field of a uniformly charged infinite plane

Let σ be the surface charge density on the plane

c) the field of two uniformly charged opposite planes

d) the field of a uniformly charged spherical surface

Electric field potential. Potential nature of electric fields.

electrostatic potential (see also Coulomb potential) - scalar energy characteristic electrostatic field, which characterizes the potential energy of the field, which has a unit charge placed at a given point in the field. The electrostatic potential is equal to the ratio of the potential energy of the interaction of the charge with the field to the value of this charge: J / C

Potential nature of electric fields.

The interaction between fixed charges is carried out by means of an electrostatic field: it is not the charges that interact, but one charge at its location interacts with the field created by another charge. This is the idea of ​​close interaction - the idea of ​​transferring interactions through a material medium, through a field.

Work on the movement of charge in an electric field. Potential difference.

A physical quantity equal to the ratio of the potential energy of an electric charge in an electrostatic field to the value of this charge is called potential

When moving a test charge q in an electric field, electric forces make work . This work for a small displacement is equal to

Electric field strength as a potential gradient. equipotential surfaces.

Gradient capacity is equal to the increment of the potential, referred to the unit length and taken in the direction in which this increment has the greatest value.

Equipotential surface is the surface on which the scalar potential of a given potential field takes on a constant value. Another, equivalent, definition is a surface, at any point orthogonal to the field lines of force.

Dipole in an electric field. Electric moment of the dipole.

uniform field

The total torque will be

inhomogeneous external field

and here a torque arises, turning the dipole along the field (Fig. 4). But in this case, the charges are affected by forces that are not the same in magnitude, the resultant of which is different from zero. Therefore, the dipole will also move forward, being drawn into the region of a stronger field

Electric moment of the dipole

Types of dielectrics. Polarization of dielectrics.

non-polar dielectric- a substance containing molecules with a predominantly covalent bond.

polar dielectric- a substance containing dipole molecules or groups, or having ions as part of the structure.

ferroelectric- a substance that contains regions with spontaneous polarization.

Polarization of dielectrics - displacement of positive and negative electric charges in dielectrics in opposite directions.

Electric field in a dielectric. Polarization vector. The field equation in a dielectric.

In a dielectric, the presence electric field does not interfere with the equilibrium of charges. The force acting on the charges in the dielectric from the electric field is balanced by intramolecular forces that hold the charges within the molecule of the dielectric, so that equilibrium of charges is possible in the dielectric, despite the presence of an electric field.

Electric polarization vector is the dipole moment per unit volume of the dielectric.

Field equation in a dielectric

where r is the density of all electric charges

Dielectric susceptibility of matter. Its relationship with the dielectric constant of the medium.

Dielectric susceptibility of matter - a physical quantity, a measure of the ability of a substance to polarize under the influence of an electric field. Dielectric susceptibility χe - coefficient of linear relationship between the polarization of the dielectric P and the external electric field E in sufficiently small fields: In the SI system: where ε0 is the electrical constant; the product ε0χe is called in the SI system the absolute dielectric susceptibility.

Ferroelectrics. Their features. Piezo effect.

ferroelectrics, crystalline dielectrics that have a spontaneous (spontaneous) polarization in a certain temperature range, which changes significantly under the influence of external influences.

Piezoelectric effect - the effect of the occurrence of dielectric polarization under the action of mechanical stresses

conductors in an electric field. Distribution of charges in a conductor.

Ε = Evext - Evint = 0

We introduce a conductor plate into an electric field, we call this field external .

As a result, there will be a negative charge on the left surface, and a positive charge on the right surface. Between these charges, an electric field will arise, which we will call internal. Inside the plate, there will simultaneously be two electric fields - external and internal, opposite in direction.

Electrical capacitance of conductors. Capacitor. Connection of capacitors.

Electrical capacity - a physical quantity numerically equal to the charge that must be imparted to a given conductor in order to increase its potential by one.

Capacitor - a device for accumulating charge and energy of the electric field.

connected in parallel

connected in series

The energy of a charged conductor, capacitor. Electric field energy. Volumetric energy density of the electric field.

The energy of a charged conductor is equal to the work that must be done to charge this conductor:

Energy of a charged capacitor

Electrostatic field energy

Volumetric energy density of the electrostatic field

16. Strength and density of the electric field. EMF. Voltage.

Current strength - scalar physical quantity, determined by the ratio of the charge Δq passing through the cross section of the conductor for a certain period of time Δt, to this period of time.

Current density j is a vector physical quantity, the modulus of which is determined by the ratio of the current strength I in the conductor to the cross-sectional area S of the conductor.

Electromotive Force (EMF) - a physical quantity that characterizes the work of external (non-potential) forces in sources of direct or alternating current. In a closed conducting circuit, the EMF is equal to the work of these forces in moving a single positive charge along the circuit.

Electrical voltage - a physical quantity, the value of which is equal to the ratio of the work of the electric field performed during the transfer of a test electric charge from point A to point B, to the value of the test charge.

17. Ohm's law for a homogeneous section of the chain. Ohm's law for an inhomogeneous section in integral form. Ohm's law for a complete circuit.

current I in a homogeneous metal conductor is directly proportional to the voltage U at the ends of this conductor and inversely proportional to the resistance R of this conductor

Ohm's law for an inhomogeneous section of a circuit in integral form IR = (φ1 - φ2) + E12

Ohm's law for a complete circuit :

18. Differential form of Ohm's law.

j-current density, σ - electrical conductivity of the substance from which the conductor is made Est-field of external forces

19. Joule-Lenz law in integral and differential forms.

in differential form:

thermal power density -

in integral form:

20. Nonlinear elements. Calculation methods with non-linear elements. Kirchhoff's rule.

non-linear electrical circuits are called, in which reactions and effects are connected non-linearly.

Simple iteration method

1. The initial non-linear equation of the electric circuit, where is the desired variable, is represented as .

2. The algorithm is calculated where

Iteration step. Linear dependencies

Here is the specified error

Kirchhoff's first rule:

the algebraic sum of the strengths of the currents converging in the node is equal to zero

Kirchhoff's second rule:

in any simple closed circuit, arbitrarily chosen in a branched electrical circuit, the algebraic sum of the products of the current strengths and the resistances of the corresponding sections is equal to the algebraic sum of the EMF present in the circuit

21. Current in vacuum. Emission phenomena and their technical applications.

Vacuum is such a state of gas in a vessel, in which the molecules fly from one wall of the vessel to another, never having experienced collisions with each other.

A vacuum insulator, the current in it can only arise due to the artificial introduction of charged particles; for this, the emission (emission) of electrons by substances is used. In vacuum lamps with heated cathodes, thermionic emission occurs, and in a photodiode, photoelectronic emission occurs.

Thermionic emission is the emission of electrons from heated metals. The concentration of free electrons in metals is quite high, therefore, even at medium temperatures, due to the distribution of electrons in terms of velocities (in terms of energies), some electrons have enough energy to overcome the potential barrier at the metal boundary. As the temperature rises, the number of electrons whose kinetic energy of thermal motion is greater than the work function increases, and the phenomenon of thermionic emission becomes noticeable.

The phenomenon of thermionic emission is used in devices in which it is necessary to obtain a flow of electrons in a vacuum, for example, in electron lamps, X-ray tubes, electron microscopes, etc. Electron lamps are widely used in electrical and radio engineering, automation and telemechanics for rectifying alternating currents, amplifying electrical signals and alternating currents, generating electromagnetic oscillations, etc. Depending on the purpose, additional control electrodes are used in the lamps.

Photoelectronic emission - this is the emission of electrons from a metal under the action of light, as well as short-wave electromagnetic radiation (for example, x-rays). The main regularities of this phenomenon will be analyzed when considering the photoelectric effect.

Secondary electron emission - this is the emission of electrons by the surface of metals, semiconductors or dielectrics when bombarded with an electron beam. The secondary electron flow consists of electrons reflected by the surface (elastically and inelastically reflected electrons) and "true" secondary electrons - electrons knocked out of a metal, semiconductor or dielectric by primary electrons.

The phenomenon of secondary electron emission is used in photomultipliers.

Field emission - this is the emission of electrons from the surface of metals under the influence of a strong external electric field. These phenomena can be observed in an evacuated tube.

22. Current in gases. Independent and non-independent conductivity of gases. CVC of current in gases. Types of discharges and their technical application.

Under normal conditions, gases are dielectrics, because. are composed of neutral atoms and molecules, and they do not have a sufficient number of free charges. To make a gas conductive, it is necessary in one way or another to introduce into it or create in it free charge carriers - charged particles. In this case, two cases are possible: either these charged particles are created by the action of some external factor or are introduced into the gas from outside, or they are created in the gas by the action of the electric field itself that exists between the electrodes. In the first case, the conductivity of the gas is called non-self-sustaining, in the second - self-sustaining.

Current-voltage characteristic (VAC ) is a graph of the dependence of the current through a two-terminal network on the voltage on this two-terminal network. The current-voltage characteristic describes the behavior of a two-terminal network at direct current.

glow discharge observed at low gas pressures. Used for cathode sputtering of metals.

spark discharge , often observed in nature, is lightning. The principle of operation of a spark voltmeter - a device for measuring very high voltages.

arc discharge can be observed under the following conditions: if, after ignition of the spark discharge, the resistance of the circuit is gradually reduced, then the current in the spark will increase. The electric arc is a powerful light source and is widely used in projection, spotlight and other lighting installations. Due to the high temperature, the arc is widely used for welding and cutting metals. The high temperature of the arc is also used in the construction of electric arc furnaces, which play an important role in modern electrometallurgy.

corona discharge observed at relatively high gas pressures (for example, at atmospheric pressure) in a sharply inhomogeneous electric field. It is used in engineering for the installation of electrostatic precipitators designed to purify industrial gases from solid and liquid impurities.

23. Magnetic field. Magnetic induction. Magnetic interaction of currents.

A magnetic field - a force field acting on moving electric charges and on bodies with a magnetic moment, regardless of the state of their movement, the magnetic component of the electromagnetic field.

Magnetic induction - vector quantity, which is a force characteristic of the magnetic field (its action on charged particles) at a given point in space. Determines the force with which the magnetic field acts on a charge moving at a speed.

Interaction of currents is caused by their magnetic fields: the magnetic field of one current acts by the Ampere force on another current and vice versa.

24. Magnetic moment of circular current. Ampere's law.

Magnetic moment of circular current the strength of the current I flowing along the coil, the area S flown by the current and the orientation of the coil in space, determined by the direction of the unit vector of the normal to the plane of the coil.

Ampère's law the law of mechanical (ponderomotive) interaction of two currents flowing in small segments of conductors located at some distance from each other.

25. Biot-Savart-Laplace law and its application to the calculation of some magnetic fields:

A) the magnetic field of a direct current-carrying conductor.

B) the field of the circular current in the center of the circular current.

Biot-Savart-Laplace law for a conductor with current I, the element dl of which creates a field induction dB at some point A, is written as where dl is a vector, modulo equal to the length dl of the conductor element and coinciding in direction with the current, r is the radius vector drawn from the element dl of the conductor to point A of the field, r is the module of the radius vector r.

magnetic induction of direct current field

magnetic induction of the field in the center of a circular conductor with current

26. Circulation of magnetic induction. Vortex nature of the magnetic current. The law of the total current in vacuum (theorem of the circulation of the induction vector).

Circulation of magnetic induction where dl is the vector of the elementary length of the contour, which is directed along the contour bypass, Bl=Bcosα is the component of the vector B in the direction of the tangent to the contour (taking into account the choice of the direction of the contour bypass), α is the angle between the vectors B and dl.

Vortex nature of the magnetic field.

The lines of magnetic induction are continuous: they have neither beginning nor end. This is the case for any magnetic field caused by any kind of current circuits. Vector fields with continuous lines are called vortex fields. We see that the magnetic field is a vortex field. This is the essential difference between a magnetic field and an electrostatic one.

The total current law for a magnetic field in vacuum (theorem of the circulation of the vector B): the circulation of the vector B along an arbitrary closed circuit is equal to the product of the magnetic constant μ0 and the algebraic sum of the currents covered by this circuit:

27. Application of the total current law to calculate the magnetic field of a solenoid.

Ring magnetic circuit

1 and coincide, hence α = 0;

2 the value of Hx is the same at all points of the contour;

3 the sum of the currents penetrating the circuit is equal to IW.

[A/m],

where Lx is the length of the contour along which the integration was carried out;

rx is the radius of the circle.

The vector inside the ring depends on the distance rx. If α is the ring width

Hav = IW / L,

where L is the length of the middle magnetic line.

28. Magnetic flux. Gauss's theorem for the flux of the magnetic induction vector.

magnetic flux - flux as an integral of the magnetic induction vector through the finite surface . Defined via the integral over the surface

In accordance with the Gauss theorem for magnetic induction, the flux of the magnetic induction vector through any closed surface is zero:

29. Work on moving a conductor and a circuit with current in a magnetic field.

work on moving a closed loop with current in a magnetic field is equal to the product of the current strength in the circuit and the change magnetic flux, linked to the contour.

30. Lorentz force. Movement of charged particles in a magnetic field. Accelerators of charged particles in a magnetic field.

Lorentz force - the force with which the electromagnetic field acts on a point charged particle. v-particle velocity

. Movement of charged particles in a magnetic field

At the heart of the accelerator the interaction of charged particles with electric and magnetic fields is laid down. An electric field is capable of directly doing work on a particle, that is, increasing its energy. The magnetic field, while creating the Lorentz force, only deflects the particle without changing its energy, and sets the orbit along which the particles move.

31. The phenomenon of electromagnetic induction. Faraday's law. Lenz's rule.

Electromagnetic induction - the phenomenon of the occurrence of an electric current in a closed circuit when the magnetic flux passing through it changes.

Faraday's law

Lenz's rule , the rule for determining the direction of the inductive current: The inductive current that occurs when the relative movement of the conducting circuit and the source of the magnetic field always has such a direction that its own magnetic flux compensates for changes in the external magnetic flux that caused this current.

32. EMF induction. The law of electromagnetic induction.

Electromotive force (EMF) - a physical quantity that characterizes the work of external (non-potential) forces in sources of direct or alternating current. In a closed conducting circuit, the EMF is equal to the work of these forces in moving a single positive charge along the circuit.

EMF can be expressed in terms of the electric field strength of external forces (Eex). In a closed loop (L) then the EMF will be equal to: , where dl is the contour length element.

Law of electromagnetic induction Email current in the circuit is possible if external forces act on the free charges of the conductor. The work of these forces to move a single positive charge along a closed loop is called EMF. When the magnetic flux changes through the surface bounded by the contour, external forces appear in the circuit, the action of which is characterized by the induction EMF.

33. Self-induction. Inductance.

self induction - excitation of the electromotive force of induction (emf) in the electrical circuit when changing electric current in this chain; special case of electromagnetic induction. The electromotive force of self-induction is directly proportional to the rate of change of current

Inductance (from Latin inductio - guidance, motivation), a physical quantity that characterizes the magnetic properties of an electrical circuit. The current flowing in a conducting circuit creates a magnetic field in the surrounding space, and the magnetic flux Ф penetrating the circuit (linked to it) is directly proportional to the current strength I:

34. The phenomenon of mutual induction. Mutual induction coefficient.

The phenomenon of mutual induction called the induction of EMF in one circuit when the current changes in another.

F21 = M21I1 Coefficient M21 is called mutual inductance the second circuit, depending on the first one.

35. Energy of the magnetic field. Magnetic field energy density.

Magnetic field energy

Magnetic field energy density (H-strength of the magnetic field).

36. Magnetic properties of matter. Matter magnetization. Gauss theorem for magnetic field induction.

By magnetic properties All substances can be divided into three classes:

substances with pronounced magnetic properties - ferromagnetic; their magnetic field is noticeable at considerable distances

paramagnetic; their magnetic properties are generally similar to those of ferromagnetic materials, but much weaker

diamagnetic substances - they are repelled by an electromagnet, i.e. the force acting on diamagnets is directed opposite to that acting on ferro- and paramagnets.

magnetization of matter

Gauss' theorem for magnetic induction

The flux of the magnetic induction vector through any closed surface is zero:

or in differential form:

This is equivalent to the fact that in nature there are no "magnetic charges" (monopoles) that would create a magnetic field, just as electric charges create an electric field. In other words, the Gauss theorem for magnetic induction shows that the magnetic field is (fully) vortex.

37. Strength of the magnetic field. Theorem on the circulation of the magnetic field strength vector.

Magnetic field strength - (standard notation H) is a vector physical quantity equal to the difference between the magnetic induction vector B and the magnetization vector M.

, where μ0 is the magnetic constant

The theorem on the circulation of the magnetic field strength vector:

The circulation of the magnetic field of direct currents in any closed circuit is proportional to the sum of the strengths of the currents penetrating the circulation circuit.

38. The law of total current in matter.

total current law : The circulation of the magnetic field strength vector along any closed loop L is equal to the algebraic sum of the macrocurrents covered by the loop.

39. Magnetic susceptibility and magnetic permeability of matter.

Magnetic permeability is a physical quantity that characterizes the relationship between magnetic induction B and magnetic field strength H in a substance.

40. Dia-, para- and feromagnets.

CM. №36

41. Electromagnetic oscillations in an oscillatory circuit. Thomson formula.

The resonant frequency of the circuit is determined by the so-called Thomson formula

Thomson formula

42. Maxwell's equation in integral form.

Using the Ostrogradsky-Gauss and Stokes formulas, Maxwell's differential equations can be given the form of integral equations:

Gauss law

Gauss' law for a magnetic field

Faraday's law of induction

What is tension really? It is a way of describing and measuring the strength of an electric field. Voltage itself cannot exist without an electronic field around positive and negative charges. Just like the magnetic field surrounds the North and South Poles.

According to modern concepts, electrons do not have mutual influence. An electric field is something that comes from one charge and its presence can be felt by another.

The same can be said about the concept of tension! It just helps us imagine what an electric field might look like. To be honest, it has no shape, no size, nothing of the sort. But the field functions with a certain force on the electrons.

Forces and their action on a charged particle

A charged electron is subjected to a force with some acceleration, causing it to move faster and faster. This force does work to move the electron.

Field lines are imaginary outlines that appear around charges (determined by the electric field), and if we place any charge in this area, it will experience a force.

Field line properties:

• travel from north to south;
• do not have mutual intersections.

Why don't two lines of force intersect? Because it doesn't happen in real life. What is being said is a physical model and nothing more. Physicists invented it to describe the behavior and characteristics of an electric field. The model is very good at this. But remembering that this is just a model, we need to know what such lines are for.

The lines of force show:

• directions of electric fields;
• tension. The closer the lines, the greater the field strength and vice versa.

If the drawn lines of force of our model intersect, the distance between them will become infinitely small. Because of the strength of the field as a form of energy, and because of the fundamental laws of physics, this is not possible.

What is potential?

Potential is the energy that is spent on the movement of a charged particle from the first point, which has zero potential, to the second point.

The potential difference between points A and B is the work done by forces to move a certain positive electron along an arbitrary trajectory from A to B.

The greater the potential of an electron, the greater the flux density per unit area. This phenomenon is similar to gravity. The greater the mass, the greater the potential, the more intense and dense the gravitational field per unit area.

A small low potential charge with a thinned flux density is shown in the following figure.

And below is a charge with a large potential and flux density.

For example: during a thunderstorm, electrons are depleted at one point and collected at another, forming an electric field. When the force becomes sufficient to break the permittivity, a lightning strike (consisting of electrons) is produced. When equalizing the potential difference, the electric field is destroyed.

electrostatic field

This is a kind of electric field, unchanging over time, formed by charges that do not move. The work of moving an electron is determined by the relations,

where r1 and r2 are the distances of the charge q to the initial and final points of the motion trajectory. According to the formula obtained, it can be seen that the work when moving a charge from point to point does not depend on the trajectory, but depends only on the beginning and end of the movement.

A force acts on each electron, and therefore, when an electron moves in a field, a certain work is performed.

In an electrostatic field, the work depends only on the final destinations, and not on the trajectory. Therefore, when the movement occurs in a closed loop, the charge comes to its original position, and the amount of work becomes equal to zero. This is because the potential drop is zero (because the electron returns to the same point). Since the potential difference is zero, the net work will also be zero, because the fall potential is equal to the work divided by the value of the charge, expressed in coulombs.

On a uniform electric field

A homogeneous electric field is called between two oppositely charged flat metal plates, where the lines of tension are parallel to each other.

Why is the force acting on a charge in such a field always the same? Thanks to symmetry. When the system is symmetrical and there is only one measurement variation, all dependence disappears. There are many other fundamental reasons for the answer, but the symmetry factor is the simplest.

The work of moving a positive charge

Electric field is the flow of electrons from "+" to "-", leading to a high intensity of the region.

Flow is the number of electric field lines passing through it. In which direction will the positive electrons move? Answer: in the direction of the electric field from positive (high potential) to negative (low potential). Therefore, a positively charged particle will move in this direction.

The intensity of the field at any point is defined as the force acting on a positive charge placed at that point.

The work consists in the transfer of electron particles along the conductor. According to Ohm's law, you can determine the work with different variations of the formulas in order to carry out the calculation.

From the law of conservation of energy it follows that work is a change in energy in a separate segment of the chain. Moving a positive charge against an electric field requires work, and the result is a gain in potential energy.

Conclusion

From the school curriculum, we remember that an electric field is formed around charged particles. Any charge in an electric field is affected by a force, and as a result, some work is done when the charge moves. A larger charge creates a larger potential, which produces a more intense or stronger electric field. This means that there is more flow and density per unit area.

The important point is that work must be done by a certain force to move the charge from a high potential to a low one. This reduces the charge difference between the poles. Moving electrons from a current to a point requires energy.

Write comments, additions to the article, maybe I missed something. Take a look at , I will be glad if you find something else useful on mine.

ELECTRIC CHARGE. ELEMENTARY PARTICLES.

Electric charge q - physical quantity that determines the intensity of electromagnetic interaction.

[q] = l Cl (Coulomb).

Atoms are made up of nuclei and electrons. The nucleus contains positively charged protons and uncharged neutrons. Electrons carry a negative charge. The number of electrons in an atom is equal to the number of protons in the nucleus, so the atom as a whole is neutral.

The charge of any body: q = ±Ne, where e \u003d 1.6 * 10 -19 C is the elementary or minimum possible charge (electron charge), N- the number of excess or missing electrons. In a closed system, the algebraic sum of the charges remains constant:

q 1 + q 2 + … + q n = const.

A point electric charge is a charged body whose dimensions are many times smaller than the distance to another electrified body interacting with it.

Coulomb's law

Two fixed point electric charges in vacuum interact with forces directed along a straight line connecting these charges; the modules of these forces are directly proportional to the product of the charges and inversely proportional to the square of the distance between them:

Proportionality factor

where is the electric constant.

where 12 is the force acting from the second charge to the first, and 21 - from the first to the second.

ELECTRIC FIELD. TENSION

The fact of the interaction of electric charges at a distance can be explained by the presence of an electric field around them - a material object, continuous in space and capable of acting on other charges.

The field of motionless electric charges is called electrostatic.

The characteristic of the field is its strength.

Electric field strength at a given point is a vector whose modulus is equal to the ratio of the force acting on a point positive charge to the magnitude of this charge, and the direction coincides with the direction of the force.

Field strength of a point charge Q on distance r from it is equal to

Principle of superposition of fields

The field strength of the system of charges is equal to the vector sum of the field strengths of each of the charges of the system:

The dielectric constant medium is equal to the ratio of field strengths in vacuum and in matter:

It shows how many times the substance weakens the field. Coulomb's law for two point charges q and Q located at a distance r in a medium with a permittivity:

Field strength at a distance r from charge Q is equal to

POTENTIAL ENERGY OF A CHARGED BODY IN A HOMOGENEOUS ELECTRIC STATIC FIELD

Between two large plates, charged with opposite signs and located in parallel, we place a point charge q.

Since the electric field between the plates with intensity is uniform, then the force acts on the charge at all points F = qE, which, when a charge moves a distance along, does work

This work does not depend on the shape of the trajectory, that is, when moving the charge q along an arbitrary line L work will be the same.

The work of an electrostatic field in moving a charge does not depend on the shape of the trajectory, but is determined exclusively by the initial and final states of the system. It, as in the case of the gravity field, is equal to the change in potential energy, taken with the opposite sign:

From a comparison with the previous formula, it can be seen that the potential energy of a charge in a uniform electrostatic field is:

Potential energy depends on the choice of the zero level and therefore has no deep meaning by itself.

ELECTROSTATIC FIELD POTENTIAL AND VOLTAGE

Potential a field is called, the work of which, when moving from one point of the field to another, does not depend on the shape of the trajectory. Potential are the gravity field and the electrostatic field.

The work done by the potential field is equal to the change in the potential energy of the system, taken with the opposite sign:

Potential- the ratio of the potential energy of the charge in the field to the value of this charge:

The potential of the homogeneous field is equal to

where d- distance counted from some zero level.

Potential charge interaction energy q is equal to the field.

Therefore, the work of the field to move the charge from a point with a potential φ 1 to a point with a potential φ 2 is:

The value is called the potential difference or voltage.

The voltage or potential difference between two points is the ratio of the work of the electric field to move the charge from the starting point to the final point to the value of this charge:

[U]=1J/Cl=1V

FIELD STRENGTH AND POTENTIAL DIFFERENCE

When moving charge q along the line of force of the electric field with a strength over a distance Δ d, the field does work

Since, by definition, we get:

Hence, the electric field strength is equal to

So, the strength of the electric field is equal to the change in potential when moving along the line of force per unit length.

If a positive charge moves in the direction of the field line, then the direction of the force coincides with the direction of movement, and the work of the field is positive:

Then , that is, the tension is directed in the direction of decreasing potential.

Tension is measured in volts per meter:

[E]=1 B/m

The field strength is 1 V/m if the voltage between two points of the field line, located at a distance of 1 m, is 1 V.

ELECTRIC CAPACITY

If we independently measure the charge Q, reported to the body, and its potential φ, it can be found that they are directly proportional to each other:

The value C characterizes the ability of the conductor to accumulate an electric charge and is called the electric capacitance. The electrical capacitance of a conductor depends on its size, shape, and the electrical properties of the medium.

The electrical capacity of two conductors is the ratio of the charge of one of them to the potential difference between them:

body capacity is 1 F if, when a charge of 1 C is imparted to it, it acquires a potential of 1 V.

CAPACITORS

Capacitor- two conductors separated by a dielectric, which serve to accumulate an electric charge. The charge of a capacitor is understood as the charge modulus of one of its plates or plates.

The ability of a capacitor to store a charge is characterized by an electrical capacity, which is equal to the ratio of the capacitor's charge to the voltage:

The capacitance of a capacitor is 1 F if, at a voltage of 1 V, its charge is 1 C.

The capacitance of a flat capacitor is directly proportional to the area of ​​the plates S, the permittivity of the medium, and is inversely proportional to the distance between the plates d:

ENERGY OF A CHARGED CAPACITOR.

Precise experiments show that W=CU 2 /2

Because q=CU, then

Electric field energy density

where V=Sd is the volume occupied by the field inside the capacitor. Given that the capacitance of a flat capacitor

and the tension on its linings U=Ed

we get:

Example. An electron, moving in an electric field from point 1 through point 2, increased its speed from 1000 to 3000 km/s. Determine the potential difference between points 1 and 2.