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Typically, an atom has same number protons and electrons. When this is the case, the atom is electrically neutral because the positively charged protons are exactly balanced by the negatively charged electrons. However, in some cases, an atom loses electrical equilibrium due to the loss or capture of an electron. When an electron is lost or captured, the atom is no longer neutral. It is either positively or negatively charged - depending on the loss or capture of an electron. Thus, a charge exists in an atom when the number of its protons and electrons do not match.
Under certain conditions, some atoms can lose a small number of electrons for a short period of time. The electrons of the atoms of some substances, especially metals, can easily be knocked out of their outer orbits. Such electrons are called free electrons, and the materials containing them are called conductors. When electrons leave an atom, the latter acquires positive charge, because a negatively charged electron is removed, disturbing the electrical balance in the atom.
An atom can just as easily capture additional electrons. In this case, it acquires a negative charge.
A charge is thus created when there is an excess of electrons or protons in an atom. When one atom is charged and the other contains a charge opposite sign, electrons can flow from one atom to another. This flow of electrons is called electric current.
An atom that has lost or gained an electron is considered unstable. The excess electrons create a negative charge in it. The lack of electrons is a positive charge. Electric charges interact with each other different ways. Two negatively charged particles repel each other, and positively charged particles also repel each other. Two charges of opposite signs attract each other. The law of electric charges states: charges with identical signs repel, and opposites attract. 1.2 serves as an illustration of the law of electric charges.
All atoms tend to remain neutral because electrons in outer orbits repel other electrons. However, many materials can acquire a positive or negative charge due to mechanical influences, such as friction. The familiar crackling sound of an ebonite comb moving through hair on a dry winter day is an example of the generation of electrical charge through friction.
« Physics - 10th grade"
First, let's consider the simplest case, when electrically charged bodies are at rest.
The branch of electrodynamics devoted to the study of the equilibrium conditions of electrically charged bodies is called electrostatics.
What's happened electric charge?
What charges are there?
With words electricity, electric charge, electricity you have met many times and managed to get used to them. But try to answer the question: “What is an electric charge?” The concept itself charge- this is a basic, primary concept that cannot be reduced to modern level development of our knowledge to some simpler, elementary concepts.
Let us first try to find out what is meant by the statement: “ This body or the particle has an electrical charge.”
All bodies are made of tiny particles, which are indivisible into simpler ones and are therefore called elementary.
Elementary particles have mass and due to this they are attracted to each other according to the law universal gravity. As the distance between particles increases, the gravitational force decreases in inverse proportion to the square of this distance. Majority elementary particles, although not all, in addition, have the ability to interact with each other with a force that also decreases inversely with the square of the distance, but this force is many times greater than the force of gravity.
So in the hydrogen atom, shown schematically in Figure 14.1, the electron is attracted to the nucleus (proton) with a force 10 39 times greater than the force of gravitational attraction.
If particles interact with each other with forces that decrease with increasing distance in the same way as the forces of universal gravity, but exceed the gravitational forces many times, then these particles are said to have an electric charge. The particles themselves are called charged.
There are particles without an electric charge, but there is no electric charge without a particle.
The interaction of charged particles is called electromagnetic.
Electric charge determines intensity electromagnetic interactions, just as mass determines the intensity of gravitational interactions.
The electric charge of an elementary particle is not a special mechanism in the particle that could be removed from it, decomposed into its component parts and reassembled. The presence of an electric charge on an electron and other particles only means the existence of certain force interactions between them.
We, in essence, know nothing about charge if we do not know the laws of these interactions. Knowledge of the laws of interactions should be included in our ideas about charge. These laws are not simple, and it is impossible to outline them in a few words. Therefore, it is impossible to give a sufficiently satisfactory short definition concept electric charge.
Two signs of electric charges.
All bodies have mass and therefore attract each other. Charged bodies can both attract and repel each other. This the most important fact, familiar to you, means that in nature there are particles with electric charges of opposite signs; in the case of charges of the same sign, the particles repel, and in the case of different signs, they attract.
Charge of elementary particles - protons, which are part of all atomic nuclei, are called positive, and the charge electrons- negative. There are no internal differences between positive and negative charges. If the signs of the particle charges were reversed, then the nature of electromagnetic interactions would not change at all.
Elementary charge.
In addition to electrons and protons, there are several other types of charged elementary particles. But only electrons and protons can exist in a free state indefinitely. The rest of the charged particles live less than a millionth of a second. They are born during collisions of fast elementary particles and, having existed for an insignificantly short time, decay, turning into other particles. You will become familiar with these particles in 11th grade.
Particles that do not have an electrical charge include neutron. Its mass is only slightly greater than the mass of a proton. Neutrons, together with protons, are part of atomic nucleus. If an elementary particle has a charge, then its value is strictly defined.
Charged bodies Electromagnetic forces in nature play a huge role due to the fact that all bodies contain electrically charged particles. The constituent parts of atoms - nuclei and electrons - have an electrical charge.
Direct action electromagnetic forces between bodies is not detected, since the bodies in their normal state are electrically neutral.
An atom of any substance is neutral because the number of electrons in it is equal to the number of protons in the nucleus. Positively and negatively charged particles are bonded to each other electrical forces and form neutral systems.
A macroscopic body is electrically charged if it contains an excess amount of elementary particles with any one sign of charge. Thus, the negative charge of a body is due to the excess number of electrons compared to the number of protons, and the positive charge is due to the lack of electrons.
In order to obtain an electrically charged macroscopic body, that is, to electrify it, it is necessary to separate part of the negative charge from the positive charge associated with it or transfer a negative charge to a neutral body.
This can be done using friction. If you run a comb through dry hair, then a small part of the most mobile charged particles - electrons - will move from the hair to the comb and charge it negatively, and the hair will charge positively.
Equality of charges during electrification
With the help of experiment, it can be proven that when electrified by friction, both bodies acquire charges that are opposite in sign, but identical in magnitude.
Let's take an electrometer, on the rod of which there is a metal sphere with a hole, and two plates on long handles: one made of hard rubber and the other made of plexiglass. When rubbing against each other, the plates become electrified.
Let's bring one of the plates inside the sphere without touching its walls. If the plate is positively charged, then some of the electrons from the needle and rod of the electrometer will be attracted to the plate and collected on inner surface spheres. At the same time, the arrow will be charged positively and will be pushed away from the electrometer rod (Fig. 14.2, a).
If you bring another plate inside the sphere, having first removed the first one, then the electrons of the sphere and the rod will be repelled from the plate and will accumulate in excess on the arrow. This will cause the arrow to deviate from the rod, and at the same angle as in the first experiment.
Having lowered both plates inside the sphere, we will not detect any deviation of the arrow at all (Fig. 14.2, b). This proves that the charges of the plates are equal in magnitude and opposite in sign.
Electrification of bodies and its manifestations. Significant electrification occurs during friction of synthetic fabrics. When you take off a shirt made of synthetic material in dry air, you can hear a characteristic crackling sound. Small sparks jump between the charged areas of the rubbing surfaces.
In printing houses, paper is electrified during printing and the sheets stick together. To prevent this from happening, special devices are used to drain the charge. However, the electrification of bodies in close contact is sometimes used, for example, in various electrocopying installations, etc.
Law of conservation of electric charge.
Experience with the electrification of plates proves that during electrification by friction, a redistribution of existing charges occurs between bodies that were previously neutral. A small portion of electrons moves from one body to another. In this case, new particles do not appear, and pre-existing ones do not disappear.
When bodies are electrified, law of conservation of electric charge. This law is valid for a system into which charged particles do not enter from the outside and from which they do not leave, i.e. for isolated system.
In an isolated system algebraic sum the charges of all bodies are conserved.
q 1 + q 2 + q 3 + ... + q n = const. (14.1)
where q 1, q 2, etc. are the charges of individual charged bodies.
The law of conservation of charge has deep meaning. If the number of charged elementary particles does not change, then the fulfillment of the charge conservation law is obvious. But elementary particles can transform into each other, be born and disappear, giving life to new particles.
However, in all cases, charged particles are born only in pairs with charges of the same magnitude and opposite in sign; Charged particles also disappear only in pairs, turning into neutral ones. And in all these cases, the algebraic sum of the charges remains the same.
The validity of the law of conservation of charge is confirmed by observations of a huge number of transformations of elementary particles. This law expresses one of the most fundamental properties of electric charge. The reason for the charge conservation is still unknown.
The word electricity comes from the Greek name for amber - ελεκτρον
.
Amber is the fossilized resin of coniferous trees. The ancients noticed that if you rub amber with a piece of cloth, it will attract light objects or dust. This phenomenon, which we today call static electricity, can be observed by rubbing an ebonite or glass rod or simply a plastic ruler with a cloth.
A plastic ruler, which has been thoroughly rubbed with a paper napkin, attracts small pieces of paper (Fig. 22.1). Rank static electricity you might have observed while combing your hair or taking off your nylon blouse or shirt. It is possible that you felt electric shock, touching a metal door handle after standing up from a car seat or walking on synthetic carpet. In all these cases, the object acquires an electrical charge through friction; they say that electrification occurs by friction.
Are all electric charges the same or are there different types? It turns out that there are two types of electric charges, which can be proven as follows: simple experience. Hang a plastic ruler by the middle on a thread and rub it thoroughly with a piece of cloth. If we now bring another electrified ruler to it, we will find that the rulers repel each other (Fig. 22.2, a).
In the same way, bringing another electrified glass rod to one, we will observe their repulsion (Fig. 22.2,6). If a charged glass rod is brought to an electrified plastic ruler, they will be attracted (Fig. 22.2, c). The ruler appears to have a different kind of charge than the glass rod.
It has been experimentally established that all charged objects are divided into two categories: either they are attracted by plastic and repelled by glass, or, conversely, repelled by plastic and attracted by glass. There appear to be two types of charges, charges of the same type repel each other, and charges different types are attracted. We say that like charges repel, and unlike charges attract.
American statesman, philosopher and scientist Benjamin Franklin (1706-1790) called these two types of charges positive and negative. It made absolutely no difference what charge to call;
Franklin proposed that the charge of an electrified glass rod be considered positive. In this case, the charge appearing on the plastic ruler (or amber) will be negative. This agreement is still followed today.
Franklin's theory of electricity was in effect a "one fluid" concept: a positive charge was seen as an excess of the "electrical fluid" over its normal content in a given object, and a negative charge as a deficiency. Franklin argued that when, as a result of some process, a certain charge arises in one body, the same amount of charge of the opposite kind simultaneously arises in another body. The names "positive" and "negative" should therefore be understood in algebraic sense, so that the total charge acquired by bodies in any process is always zero.
For example, when a plastic ruler is rubbed with a paper napkin, the ruler acquires a negative charge, and the napkin acquires an equal positive charge. There is a separation of charges, but their sum is zero.
This example illustrates the firmly established law of conservation of electric charge, which reads:
The total electric charge resulting from any process is zero.
Deviations from this law have never been observed, therefore we can consider that it is as firmly established as the laws of conservation of energy and momentum.
Electric charges in atoms
Only in the last century did it become clear that the reason for the existence of electric charge lies in the atoms themselves. Later we will discuss the structure of the atom and the development of ideas about it in more detail. Here we will briefly discuss the main ideas that will help us better understand the nature of electricity.
By modern ideas an atom (somewhat simplified) consists of a heavy, positively charged nucleus surrounded by one or more negatively charged electrons.
IN in good condition the positive and negative charges in an atom are equal in magnitude, and the atom as a whole is electrically neutral. However, an atom can lose or gain one or more electrons. Then its charge will be positive or negative, and such an atom is called an ion.
In a solid, nuclei can vibrate, remaining near fixed positions, while some electrons move completely freely. Electrification by friction can be explained by the fact that in various substances Nuclei hold electrons with different strengths.
When a plastic ruler that is rubbed with a paper napkin becomes negatively charged, it means that the electrons in paper napkin are retained weaker than in plastic, and some of them transfer from the napkin to the ruler. The positive charge of the napkin is equal in magnitude to the negative charge acquired by the ruler.
Typically, objects electrified by friction only hold a charge for a while and eventually return to an electrically neutral state. Where does the charge go? It “drains” onto the water molecules contained in the air.
The fact is that water molecules are polar: although in general they are electrically neutral, the charge in them is not uniformly distributed (Fig. 22.3). Therefore, excess electrons from the electrified ruler will “drain” into the air, being attracted to the positively charged region of the water molecule.
On the other hand, the positive charge of the object will be neutralized by electrons, which are weakly held by water molecules in the air. In dry weather, the influence of static electricity is much more noticeable: the air contains fewer molecules water and the charge does not drain so quickly. In damp, rainy weather, the item is unable to hold its charge for long.
Insulators and conductors
Let there be two metal balls, one of which is highly charged and the other is electrically neutral. If we connect them with, say, an iron nail, the uncharged ball will quickly acquire an electric charge. If we simultaneously touch both balls with a wooden stick or a piece of rubber, then the ball, which had no charge, will remain uncharged. Substances such as iron are called conductors of electricity; wood and rubber are called non-conductors, or insulators.
Metals are generally good conductors; Most other substances are insulators (however, insulators conduct electricity a little). It's interesting that almost everyone natural materials fall into one of these two sharply different categories.
There are, however, substances (among which silicon, germanium and carbon should be mentioned) that belong to an intermediate (but also sharply separated) category. They are called semiconductors.
From point of view atomic theory electrons in insulators are bound to the nuclei very tightly, while in conductors many electrons are bound very loosely and can move freely within the substance.
When a positively charged object is brought close to or touches a conductor, free electrons quickly move toward the positive charge. If an object is negatively charged, then electrons, on the contrary, tend to move away from it. In semiconductors there are very few free electrons, and in insulators they are practically absent.
Induced charge. Electroscope
Let's bring a positively charged metal object to another (neutral) metal object.
Upon contact, free electrons of a neutral object will be attracted to a positively charged one and some of them will transfer to it. Since the second object now lacks a certain number of negatively charged electrons, it acquires a positive charge. This process is called electrification due to electrical conductivity.
Let us now bring the positively charged object closer to the neutral metal rod, but so that they do not touch. Although the electrons will not leave the metal rod, they will nevertheless move towards the charged object; a positive charge will arise at the opposite end of the rod (Fig. 22.4). In this case, it is said that a charge is induced (or induced) at the ends of the metal rod. Of course, no new charges arise: the charges simply separated, but on the whole the rod remained electrically neutral. However, if we were now to cut the rod crosswise in the middle, we would get two charged objects - one with a negative charge, the other with a positive charge.
You can also impart a charge to a metal object by connecting it with a wire to the ground (or, for example, to a water pipe going into the ground), as shown in Fig. 22.5, a. The subject is said to be grounded. Due to its enormous size, the earth accepts and gives up electrons; it acts as a charge reservoir. If you bring a charged, say, negatively, object close to the metal, then the free electrons of the metal will be repelled and many will go along the wire into the ground (Fig. 22.5,6). The metal will be positively charged. If you now disconnect the wire, a positive induced charge will remain on the metal. But if you do this after the negatively charged object is removed from the metal, then all the electrons will have time to return back and the metal will remain electrically neutral.
An electroscope (or simple electrometer) is used to detect electrical charge.
As can be seen from Fig. 22.6, it consists of a body, inside of which there are two movable leaves, often made of gold. (Sometimes only one leaf is made movable.) The leaves are mounted on a metal rod, which is insulated from the body and ends on the outside with a metal ball. If you bring a charged object close to the ball, a separation of charges occurs in the rod (Fig. 22.7, a), the leaves turn out to be similarly charged and repel each other, as shown in the figure.
You can completely charge the rod due to electrical conductivity (Fig. 22.7, b). In any case, the greater the charge, the more the leaves diverge.
Note, however, that the sign of the charge cannot be determined in this way: a negative charge will separate the leaves exactly the same distance as an equal positive charge. And yet, an electroscope can be used to determine the sign of the charge; for this, the rod must first be given, say, a negative charge (Fig. 22.8, a). If you now bring a negatively charged object to the electroscope ball (Fig. 22.8,6), then additional electrons will move to the leaves and they will move apart further. On the contrary, if a positive charge is brought to the ball, then the electrons will move away from the leaves and they will come closer (Fig. 22.8, c), since their negative charge will decrease.
The electroscope was widely used at the dawn of electrical engineering. Very sensitive modern electrometers operate on the same principle when using electronic circuits.
This publication is based on materials from the book by D. Giancoli. "Physics in two volumes" 1984 Volume 2.
To be continued. Briefly about the following publication:
Force F, with which one charged body acts on another charged body, is proportional to the product of their charges Q 1 and Q 2 and inversely proportional to the square of the distance r between them.
Comments and suggestions are accepted and welcome!
3.1. Electric charge
Even in ancient times, people noticed that a piece of amber worn with wool began to attract various small objects: specks of dust, threads, and the like. You can easily see for yourself that a plastic comb, rubbed against your hair, begins to attract small pieces of paper. This phenomenon is called electrification, and the forces acting in this case are electrical forces. Both names come from Greek word"electron", which means "amber".
When rubbing a comb on hair or an ebonite stick on wool objects charging, they form electric charges. Charged bodies interact with each other and electrical forces arise between them.
Not only solids, but also liquids and even gases can be electrified by friction.
When bodies are electrified, the substances that make up the electrified bodies do not transform into other substances. Thus, electrification is a physical phenomenon.
There are two different kinds electric charges. Quite arbitrarily they are named " positive" charge and " negative" charge (and one could call them “black” and “white”, or “beautiful” and “terrible”, or something else).
Positively charged call bodies that act on other charged objects in the same way as glass electrified by friction with silk.
Negatively charged call bodies that act on other charged objects in the same way as sealing wax electrified by friction on wool.
The main property of charged bodies and particles: Likely charged bodies and particles repel, and oppositely charged bodies attract.
In experiments with sources of electric charges, you will become familiar with some other properties of these charges: charges can “flow” from one object to another, accumulate, an electric discharge can occur between charged bodies, and so on. You will study these properties in detail in a physics course.
3.2. Coulomb's law
Electric charge ( Q or q) is a physical quantity, it can be larger or smaller, and therefore can be measured. But physicists are not yet able to directly compare charges with each other, so they compare not the charges themselves, but the effect that charged bodies have on each other, or on other bodies, for example, the force with which one charged body acts on another.
The forces (F) acting on each of the two point charged bodies are oppositely directed along the straight line connecting these bodies. Their values are equal to each other, directly proportional to the product of the charges of these bodies (q 1 ) and (q 2 ) and are inversely proportional to the square of the distance (l) between them.
This relationship is called "Coulomb's law" in honor of the French physicist Charles Coulomb (1763-1806) who discovered it in 1785. The dependence of Coulomb forces on the sign of the charge and the distance between charged bodies, which is most important for chemistry, is clearly shown in Fig. 3.1.
The unit of measurement of electric charge is the coulomb (definition in a physics course). A charge of 1 C flows through a 100-watt light bulb in about 2 seconds (at a voltage of 220 V).
3.3. Elementary electric charge
Before late XIX centuries, the nature of electricity remained unclear, but numerous experiments led scientists to the conclusion that the magnitude of the electric charge cannot change continuously. It was found that there is a smallest, further indivisible portion of electricity. The charge of this portion is called "elementary electric charge" (denoted by the letter e). It turned out to be 1.6. 10–19 Grades This is a very small value - almost 3 billion billion elementary electrical charges pass through the filament of the same light bulb in 1 second.
Any charge is a multiple of the elementary electric charge, so it is convenient to use the elementary electric charge as a unit of measurement for small charges. Thus,
1e= 1.6. 10–19 Grades
On turn of the 19th century and XX centuries, physicists realized that the carrier of an elementary negative electric charge is a microparticle, called electron(Joseph John Thomson, 1897). The carrier of an elementary positive charge is a microparticle called proton- was discovered a little later (Ernest Rutherford, 1919). At the same time it was proven that positive and negative elementary electric charges are equal in absolute value
Thus, the elementary electric charge is the charge of a proton.
You will learn about other characteristics of the electron and proton in the next chapter.
Despite the fact that the composition of physical bodies includes charged particles, in the normal state the bodies are uncharged, or electrically neutral. Many complex particles, such as atoms or molecules, are also electrically neutral. The total charge of such a particle or such a body turns out to be zero because the number of electrons and the number of protons included in the composition of the particle or body are equal.
Bodies or particles become charged if electric charges are separated: on one body (or particle) there is an excess of electric charges of one sign, and on the other - of another. In chemical phenomena, an electric charge of any one sign (positive or negative) can neither appear nor disappear, since carriers of elementary electric charges of only one sign cannot appear or disappear.
POSITIVE ELECTRIC CHARGE, NEGATIVE ELECTRIC CHARGE, BASIC PROPERTIES OF CHARGED BODIES AND PARTICLES, COULLOMB'S LAW, ELEMENTARY ELECTRIC CHARGE
1.How is silk charged when rubbed against glass? What about wool when rubbed against sealing wax?
2.What number of elementary electric charges makes up 1 coulomb?
3. Determine the force with which two bodies with charges +2 C and –3 C, located at a distance of 0.15 m from each other, are attracted to each other.
4. Two bodies with charges +0.2 C and –0.2 C are at a distance of 1 cm from each other. Determine the force with which they attract.
5. With what force do two particles carrying each other repel each other? same charge, equal to +3 e, and located at a distance of 2 E? The value of the constant in the equation of Coulomb's law k= 9. 10 9 N. m 2 / Cl 2.
6. With what force is an electron attracted to a proton if the distance between them is 0.53 E? What about proton to electron?
7.Two like and identically charged balls are connected by a non-conducting thread. The middle of the thread is fixedly fixed. Draw how these balls will be located in space under conditions where the force of gravity can be neglected.
8. Under the same conditions, how will three identical balls, tied by threads of equal length to one support, be located in space? How about four?
Experiments on attraction and repulsion of charged bodies.
Electric charge– a physical quantity characterizing the ability of bodies to enter into electromagnetic interactions. Measured in Coulombs.
Elementary electric charge– the minimum charge that elementary particles have (proton and electron charge).
The body has a charge, means it has extra or missing electrons. This charge is designated q=ne. (He equal to the number elementary charges).
Electrify the body– create an excess and deficiency of electrons. Methods: electrification by friction And electrification by contact.
Point dawn d is the charge of the body, which can be taken as a material point.
Test charge(
) – point, small charge, always positive – used for research electric field.
Law of conservation of charge:in an isolated system, the algebraic sum of the charges of all bodies remains constant for any interactions of these bodies with each other.
Coulomb's law:the forces of interaction between two point charges are proportional to the product of these charges, inversely proportional to the square of the distance between them, depend on the properties of the medium and are directed along the straight line connecting their centers.
, Where 
F/m, Cl 2 /nm 2 – dielectric. fast. vacuum
- relates. dielectric constant (>1)
- absolute dielectric permeability. environment
Electric field– a material medium through which the interaction of electric charges occurs.
Electric field properties:
Electric field characteristics:
Tension(E) – vector quantity, equal to strength, acting on a unit test charge placed at a given point.
Measured in N/C. 
Direction– the same as that of the acting force.
Tension does not depend neither on the strength nor on the size of the test charge.
Superposition of electric fields: the field strength created by several charges is equal to the vector sum of the field strengths of each charge:
Graphically The electronic field is represented using tension lines.
Tension line– a line whose tangent at each point coincides with the direction of the tension vector.
Properties of tension lines: they do not intersect, only one line can be drawn through each point; they are not closed, they leave a positive charge and enter a negative one, or dissipate into infinity.
Types of fields:
Uniform electric field– a field whose intensity vector at each point is the same in magnitude and direction.
Non-uniform electric field– a field whose intensity vector at each point is unequal in magnitude and direction.
Constant electric field– the tension vector does not change.
Variable electric field– the tension vector changes.
Work done by an electric field to move a charge.
, where F is force, S is displacement, 
- angle between F and S.
For uniform field: force is constant.
The work does not depend on the shape of the trajectory; the work done to move along a closed path is zero.
For a non-uniform field:
Electric field potential– the ratio of the work that the field does, moving a test electric charge to infinity, to the magnitude of this charge.
-potential– energy characteristic of the field. Measured in Volts
Potential difference:
If 
, That 
, Means 
-potential gradient.
For a uniform field: potential difference – voltage:
. It is measured in Volts, the devices are voltmeters.
Electrical capacity– the ability of bodies to accumulate electrical charge; the ratio of charge to potential, which is always constant for a given conductor.
.
Does not depend on charge and does not depend on potential. But it depends on the size and shape of the conductor; on the dielectric properties of the medium.
, where r is the size, 
- permeability of the environment around the body.
Electrical capacity increases if any bodies - conductors or dielectrics - are nearby.
Capacitor– device for accumulating charge. Electrical capacity: 
Flat capacitor– two metal plates with a dielectric between them. Electric capacity of a flat capacitor:
, where S is the area of the plates, d is the distance between the plates.
Energy of a charged capacitor equal to the work done by the electric field when transferring charge from one plate to another.
Small charge transfer 
, the voltage will change to 
, the work is done 
. Because 
, and C =const, 
. Then 
. Let's integrate:
Electric field energy:
, where V=Sl is the volume occupied by the electric field
For a non-uniform field:
.
Volumetric electric field density:
. Measured in J/m 3.
Electric dipole– a system consisting of two equal, but opposite in sign, point electric charges located at some distance from each other (dipole arm -l).
The main characteristic of a dipole is dipole moment– a vector equal to the product of the charge and the dipole arm, directed from the negative charge to the positive one. Designated 
. Measured in Coulomb meters.
Dipole in a uniform electric field.
The following forces act on each charge of the dipole: 
And 
. These forces are oppositely directed and create a moment of a pair of forces - a torque:, where
M – torque F – forces acting on the dipole
d – sill arm – dipole arm
p – dipole moment E – tension
- angle between p Eq – charge
Under the influence of a torque, the dipole will rotate and align itself in the direction of the tension lines. Vectors p and E will be parallel and unidirectional.
Dipole in a non-uniform electric field.
There is a torque, which means the dipole will rotate. But the forces will be unequal, and the dipole will move to where the force is greater.
-tension gradient. The higher the tension gradient, the higher the lateral force that pulls the dipole. The dipole is oriented along the lines of force.
Dipole intrinsic field.
But . Then:
.
Let the dipole be at point O and its arm small. Then:
.
The formula was obtained taking into account: 
Thus, the potential difference depends on the sine half angle, under which the dipole points are visible, and the projections of the dipole moment onto the straight line connecting these points.
Dielectrics in an electric field.
Dielectric- a substance that does not have free charges, and therefore does not conduct electric current. However, in fact, conductivity exists, but it is negligible.
Dielectric classes:
with polar molecules (water, nitrobenzene): the molecules are not symmetrical, the centers of mass of positive and negative charges do not coincide, which means they have a dipole moment even in the case when there is no electric field.
with non-polar molecules (hydrogen, oxygen): the molecules are symmetrical, the centers of mass of positive and negative charges coincide, which means they do not have a dipole moment in the absence of an electric field.
crystalline (sodium chloride): a combination of two sublattices, one of which is positively charged and the other negatively charged; in the absence of an electric field, the total dipole moment is zero.
Polarization– the process of spatial separation of charges, the appearance of bound charges on the surface of the dielectric, which leads to a weakening of the field inside the dielectric.
Polarization methods:
Method 1 – electrochemical polarization:
On the electrodes – movement of cations and anions towards them, neutralization of substances; areas of positive and negative charges are formed. The current gradually decreases. The rate of establishment of the neutralization mechanism is characterized by the relaxation time - this is the time during which the polarization emf increases from 0 to a maximum from the moment the field is applied. 
= 10 -3 -10 -2 s.
Method 2 – orientational polarization:
Uncompensated polar ones are formed on the surface of the dielectric, i.e. the phenomenon of polarization occurs. The voltage inside the dielectric is less than the external voltage. Relaxation time: 
= 10 -13 -10 -7 s. Frequency 10 MHz.
Method 3 – electronic polarization:
Characteristic of non-polar molecules that become dipoles. Relaxation time: 
= 10 -16 -10 -14 s. Frequency 10 8 MHz.
Method 4 – ion polarization:
Two lattices (Na and Cl) are displaced relative to each other.
Relaxation time: 
Method 5 – microstructural polarization:
Characteristic of biological structures when charged and uncharged layers alternate. There is a redistribution of ions on semi-permeable or ion-impermeable partitions.
Relaxation time: 
=10 -8 -10 -3 s. Frequency 1KHz
Numerical characteristics of the degree of polarization:
Electricity– this is the ordered movement of free charges in matter or in a vacuum.
Conditions for the existence of electric current:
presence of free charges
the presence of an electric field, i.e. forces acting on these charges
Current strength– a value equal to the charge that passes through any cross section of a conductor per unit of time (1 second)
Measured in Amperes.
n – charge concentration
q – charge value
S – cross-sectional area of the conductor
- speed of directional movement of particles.
The speed of movement of charged particles in an electric field is small - 7 * 10 -5 m/s, the speed of propagation of the electric field is 3 * 10 8 m/s.
Current Density– the amount of charge passing through a cross section of 1 m2 in 1 second.
. Measured in A/m2.
- the force acting on the ion from the electric field is equal to the friction force
- ion mobility
- speed of directional movement of ions = mobility, field strength
The greater the concentration of ions, their charge and mobility, the greater the specific conductivity of the electrolyte. As the temperature increases, the mobility of ions increases and the electrical conductivity increases.