Electricity and magnetism

LECTURE 11

ELECTROSTATICS

Electric charge

A large number of phenomena in nature are associated with the manifestation of a special property of elementary particles of matter - the presence of an electric charge. These phenomena were called electric And magnetic.

The word "electricity" comes from the Greek hlectron - electron (amber). The ability of rubbed amber to acquire a charge and attract light objects was noted in ancient Greece.

The word “magnetism” comes from the name of the city of Magnesia in Asia Minor, near which the properties of iron ore (magnetic iron ore FeO∙Fe 2 O 3) were discovered to attract iron objects and impart magnetic properties to them.

The doctrine of electricity and magnetism is divided into sections:

a) the study of stationary charges and the constant electric fields associated with them - electrostatics;

b) the doctrine of uniformly moving charges - direct current and magnetism;

c) the study of unevenly moving charges and the alternating fields created in this case - alternating current and electrodynamics, or the theory of the electromagnetic field.

Electrification by friction

A glass rod rubbed with leather or an ebonite rod rubbed with wool acquires an electric charge or, as they say, becomes electrified.

Elder balls (Fig. 11.1), which are touched with a glass rod, are repelled. If you touch them with an ebonite stick, they also repel. If you touch one of them with an ebonite rod and the other with a glass rod, they will be attracted.

Therefore, there are two types of electric charges. The charges arising on glass rubbed by leather are called positive (+). The charges arising on ebonite rubbed with wool are agreed to be called negative (-).

Experiments show that like charges (+ and +, or – and -) repel, while unlike charges (+ and -) attract.

Point charge called a charged body, the dimensions of which can be neglected in comparison with the distances at which the effect of this charge on other charges is considered. A point charge is an abstraction, like a material point in mechanics.

Law of point interaction

Charges (Coulomb's law)

In 1785, the French scientist Auguste Coulomb (1736-1806), based on experiments with torsion balances, at the end of the beam of which charged bodies were placed, and then other charged bodies were brought to them, established a law that determines the force of interaction between two stationary point objects. charges Q 1 and Q 2, the distance between them r.

Coulomb's law in a vacuum states: interaction force F between two stationary point charges located in a vacuum proportional to charges Q 1 and Q 2 and inversely proportional to the square of the distance r between them:

,

where is the coefficient k depends on the choice of the system of units and the properties of the medium in which the interaction of charges occurs.

The quantity showing how many times the force of interaction between charges in a given dielectric is less than the force of interaction between them in a vacuum is called relative dielectric constant of the medium e.

Coulomb's law for interaction in a medium: interaction force between two point charges Q 1 and Q 2 is directly proportional to the product of their values ​​and inversely proportional to the product of the dielectric constant of the medium e. per square of distance r between charges:

.

In the SI system , where e 0 is the dielectric constant of vacuum, or the electric constant. Magnitude e 0 refers to the number fundamental physical constants and is equal to e 0 =8.85∙10 -12 Cl 2 /(N∙m 2), or e 0 =8.85∙10 -12 F/m, where farad(F) - unit of electrical capacitance. Then .

Taking into account k Coulomb's law will be written in its final form:

,

Where ee 0 =e a is the absolute dielectric constant of the medium.

Coulomb's law in vector form.

,

Where F 12 - force acting on the charge Q 1 charge side Q 2 , r 12 - radius vector connecting the charge Q 2 with charge Q 1, r=|r 12 | (Fig. 11.1).

Per charge Q 2 charge side Q 1 force acts F 21 =-F 12, i.e. Newton's 3rd law is true.

11.4. Law of Conservation of Electricity

Charge

From a generalization of experimental data, it was established fundamental law of nature experimentally confirmed in 1843 by the English physicist Michael Faraday (1791-1867), - law of conservation of charge.

The law states: the algebraic sum of the electric charges of any closed system (a system that does not exchange charges with external bodies) remains unchanged, no matter what processes occur within this system:

.

The law of conservation of electric charge is strictly observed both in macroscopic interactions, for example, during the electrification of bodies by friction, when both bodies are charged with numerically equal charges of opposite signs, and in microscopic interactions, in nuclear reactions.

Electrification of the body through influence(electrostatic induction). When a charged body is brought to an insulated conductor, a separation of charges occurs on the conductor (Fig. 79).

If the charge induced at the remote end of the conductor is taken to the ground, and then, having previously removed the grounding, the charged body is removed, then the charge remaining on the conductor will be distributed throughout the conductor.

Experimentally (1910-1914), the American physicist R. Millikan (1868-1953) showed that the electric charge is discrete, i.e. the charge of any body is an integer multiple of the elementary electric charge e(e=1.6∙10 -19 C). Electron (i.e. = 9.11∙10 -31 kg) and proton ( m p=1.67∙10 -27 kg) are respectively carriers of elementary negative and positive charges.

Electrostatic field.

Tension

Fixed charge Q inextricably linked with the electric field in the space surrounding it. Electric field is a special type of matter and is a material carrier of interaction between charges even in the absence of substance between them.

Electric charge field Q acts with force F on a test charge placed at any point in the field Q 0 .

Electric field strength. The electric field strength vector at a given point is a physical quantity determined by the force acting on a test unit positive charge placed at this point in the field:

.

Field strength of a point charge in vacuum

.

Vector direction E coincides with the direction of the force acting on the positive charge. If the field is created by a positive charge, then the vector E directed along the radius vector from the charge into external space (repulsion of the test positive charge); if the field is created by a negative charge, then the vector E directed towards the charge (Fig. 11.3).

The unit of electric field strength is newton per coulomb (N/C): 1 N/C is the intensity of the field that acts on a point charge of 1 C with a force of 1 N; 1 N/C=1 V/m, where V (volt) is the unit of electrostatic field potential.

Tension lines.

Lines whose tangents at each point coincide in direction with the tension vector at that point are called lines of tension(Fig. 11.4).

Point charge field strength q on distance r from it in the SI system:

.

The field strength lines of a point charge are rays emanating from the point where the charge is placed (for a positive charge) or entering it (for a negative charge) (Fig. 11.5, a, b ).

In order to use tension lines to characterize not only the direction, but also the value of the electrostatic field strength, it was agreed to draw them with a certain density (see Fig. 11.4): the number of tension lines penetrating a unit surface area perpendicular to the tension lines must be equal to the modulus vector E. Then the number of tension lines penetrating the elementary area d S, normal n which forms an angle a with the vector E, equals E d Scos a =E n d S, Where E n - vector projection E to normal n to site d S(Fig. 11.6). Magnitude

called flow of the tension vector through platform d S. The flux unit of the electrostatic field strength vector is 1 V∙m.

For an arbitrary closed surface S vector flow E through this surface

, (11.5)

where the integral is taken over a closed surface S. Flow vector E is algebraic quantity: depends not only on the field configuration E, but also on the choice of direction n.

The principle of superposition of electrical

fields

If the electric field is created by charges Q 1 ,Q 2 , … , Qn, then for a test charge Q 0 force applied F equal to the vector sum of forces F i , applied to it from each of the charges Qi :

.

The vector of the electric field strength of a system of charges is equal to the geometric sum of the field strengths created by each of the charges separately:

.

This principle superposition (imposition) of electrostatic fields.

The principle states: tension E the resulting field created by the system of charges is equal to geometric sum field strengths created at a given point by each of the charges separately.

The principle of superposition allows one to calculate the electrostatic fields of any system of stationary charges, since if the charges are not point charges, then they can always be reduced to a set of point charges.

The main task of electrostatics is formulated as follows: given the distribution in space of field sources - electric charges - find the value of the intensity vector at all points of the field. This problem can be solved based on superposition principle electric fields.

The electric field strength of a system of charges is equal to the geometric sum of the field strengths of each of the charges separately.

Charges can be distributed in space either discretely or continuously. In the first case, the field strength for a system of point charges

where is the field strength i th charge of the system at the considered point in space, n is the total number of discrete charges of the system.

If electric charges are continuously distributed along the line, then linear density is introduced charges t, Kl/m.

t = (dq/dl),

Where dq- charge of a small section length dl.

If electric charges are continuously distributed over the surface, then the surface charge density is introduced s, C/m 2 .

s = (dq/dS),

Where dq- a charge located on a small surface area of dS.

With a continuous distribution of charges in any volume, the volumetric charge density is introduced r, C/m 3 .

r = (dq/dV),

Where dq- charge located in a small volume element dV.

According to the principle of superposition, the strength of the electrostatic field created in a vacuum by continuously distributed charges:

where is the strength of the electrostatic field created in a vacuum by a small charge dq, and integration is carried out over all continuously distributed charges.

Let's consider the application of the superposition principle to an electric dipole.

An electric dipole is a system of two electric charges equal in absolute value and opposite in sign ( q and –q), distance l between which there is little compared to the distance to the field points under consideration. The vector directed along the dipole axis from the negative to the positive charge is called the dipole arm. The vector is called the electric moment of the dipole (dipole electric moment). Dipole field strength at an arbitrary point , where and are the field strengths of charges q and -q (Fig. 1.2).

At point A, located on the dipole axis at a distance r from its center ( r>>l), dipole field strength in vacuum:

At point B, located on a perpendicular restored to the dipole axis from its middle, at a distance r from the center ( r>>l):

At an arbitrary point C, the modulus of the tension vector

Where r- the value of the radius vector drawn from the center of the dipole to point C; a is the angle between the radius vector and the dipole moment (Fig. 1.2).

1.3. Flow of tension. Gauss's theorem for the electrostatic field in vacuum

Elementary flow of electric field strength through a small area of ​​surface area dS drawn in the field is called a scalar physical quantity

dN = = EdScos() = E n dS = EdS ^ ,

where is the vector of electric field strength at the site dS, - unit vector normal to the site dS, -site vector, E n = Ecos()- projection of the vector onto the direction of the vector , dS^ = dScos()- element projection area dS surface onto a plane perpendicular to the vector (Fig. 1.3).

Gauss's theorem

The flow of electrostatic field strength in a vacuum through an arbitrary closed surface is proportional to the algebraic sum of the electric charges covered by this surface:

where all vectors are directed along the outer normals to the closed integration surface S which is often called Gaussian surface.

1.4. Electrostatic field potential. The work done by the forces of an electrostatic field when an electric charge moves through it

Job dA, accomplished by Coulomb forces with a small displacement of a point charge q in an electrostatic field:

where is the field strength at the location of the charge q. Work done by the Coulomb force when moving a charge q from point 1 to point 2 does not depend on the shape of the charge trajectory (i.e. Coulomb forces are conservative forces). Work done by electrostatic field forces when moving a charge q along any closed contour L equal to zero. This can be written as circulation theorems vector of electrostatic field strength.

The circulation of the electrostatic field strength vector is zero:

This relationship, expressing the potential nature of the electrostatic field, is valid both in vacuum and in matter.

Job dA, accomplished by the forces of an electrostatic field with a small movement of a point charge q in an electrostatic field, is equal to the decrease in the potential energy of this charge in the field:

dA= - dW P and A 12 = - DW P = W P1 - W P2,

Where W P1 And W P2- values ​​of potential charge energy q at points 1 and 2 of the field. The energy characteristic of an electrostatic field is its potential.

Potential electrostatic field is a scalar physical quantity j, equal to potential energy W P positive unit point charge placed at the field point under consideration, V.

Field potential of a point charge q in vacuum

Superposition principle for potential

those. When electrostatic fields are applied, their potentials add up algebraically.

Electric dipole field potential at point C (Fig. 1.2)

If the charges are distributed continuously in space, then the potential j their fields in vacuum:

Integration is carried out over all charges forming the system under consideration.

Job A 12, accomplished by electrostatic field forces when moving a point charge q from point 1 of the field (potential j 1) to point 2 (potential j 2):

A 12 = q (j 1 - j 2).

If j 2= 0, then .

Potential any point in the electrostatic field is numerically equal to the work done by field forces when moving a positive unit charge from a given point to a point in the field where the potential is assumed to be zero.

When studying electrostatic fields at certain points, the differences are important, not the absolute values ​​of the potentials at these points. Therefore, the choice of a point with zero potential is determined only by the convenience of solving this problem. The relationship between potential and tension has the form

E x = , E y = , E z= and ,

those. the electrostatic field strength is equal in magnitude and opposite in direction to the potential gradient.

The geometric location of the points of the electrostatic field at which the potential values ​​are the same is called the equipotential surface . If the vector is directed tangent to the equipotential surface, then And . This means that the intensity vector is perpendicular to the equipotential surface at each point, i.e. E = E n.

1.5. Examples of application of Gauss's theorem to the calculation of electrostatic fields s >0) or to it (if s < 0).

For all field points

Since , and assuming the field potential equal to zero at points of the charged plane ( X= 0), we get

Dependency graphs E And j from x are shown in Fig. 1.6.

Let there be two charged macroscopic bodies, the sizes of which are negligible compared to the distance between them. In this case, each body can be considered a material point or a “point charge”.

The French physicist C. Coulomb (1736–1806) experimentally established the law that bears his name ( Coulomb's law) (Fig. 1.5):

Rice. 1.5. C. Coulon (1736–1806) - French engineer and physicist

In a vacuum, the force of interaction between two stationary point charges is proportional to the size of each of the charges, inversely proportional to the square of the distance between them and directed along the straight line connecting these charges:

In Fig. Figure 1.6 shows the electrical repulsive forces that arise between two point charges of the same name.

Rice. 1.6. Electrical repulsive forces between two like point charges

Let us recall that , where and are the radius vectors of the first and second charges, therefore the force acting on the second charge as a result of its electrostatic - “Coulomb” interaction with the first charge can be rewritten in the following “expanded” form

Let us note the following rule, convenient for solving problems: if the first index of the force is the number of that charge, on which this force acts, and the second is the number of that charge, which creates this force, then compliance with the same order of indices on the right side of the formula automatically ensures the correct direction of the force - corresponding to the sign of the product of charges: - repulsion and - attraction, while the coefficient is always.

To measure the forces acting between point charges, a device created by Coulomb, called torsion scales(Fig. 1.7, 1.8).

Rice. 1.7. Torsion scales by Ch. Coulomb (drawing from the work of 1785). The force acting between charged balls a and b was measured

Rice. 1.8. Torsion scales Sh. Coulomb (suspension point)

A light rocker arm is suspended from a thin elastic thread, with a metal ball attached at one end and a counterweight at the other. Next to the first ball, you can place another identical motionless ball. The glass cylinder protects sensitive parts of the device from air movement.

To establish the dependence of the strength of electrostatic interaction on the distance between charges, the balls are given arbitrary charges by touching them with a third charged ball mounted on a dielectric handle. Using the angle of twist of the elastic thread, you can measure the repulsive force of similarly charged balls, and using the scale of the device, you can measure the distance between them.

It must be said that Coulomb was not the first scientist to establish the law of interaction of charges, which now bears his name: 30 years before him, B. Franklin came to the same conclusion. Moreover, the accuracy of Coulomb's measurements was inferior to the accuracy of previously conducted experiments (G. Cavendish).

To introduce a quantitative measure to determine the accuracy of measurements, let us assume that in fact the force of interaction between charges is not the inverse of the square of the distance between them, but some other power:

None of the scientists will undertake to claim that d= 0 exactly. The correct conclusion should be: experiments have shown that d does not exceed...

The results of some of these experiments are shown in Table 1.

Table 1.

Results of direct experiments to test Coulomb's law

Charles Coulomb himself tested the inverse square law to within a few percent. The table shows the results of direct laboratory experiments. Indirect evidence based on observations of magnetic fields in space leads to even stronger restrictions on the magnitude d. Thus, Coulomb's law can be considered a reliably established fact.

The SI unit of current is ( ampere) is basic, hence the unit of charge q turns out to be a derivative. As we will see later, the current strength I is defined as the ratio of the charge flowing through the cross-section of the conductor in time to this time:

From this it can be seen that the strength of the direct current is numerically equal to the charge flowing through the cross section of the conductor per unit time, according to this:

The proportionality coefficient in Coulomb's law is written as:

With this form of recording, the value of the quantity follows from the experiment, which is usually called electrical constant. The approximate numerical value of the electrical constant is as follows:

Since it most often appears in equations as a combination

Let's give the numerical value of the coefficient itself

As in the case of an elementary charge, the numerical value of the electric constant is determined experimentally with high accuracy:

The coulomb is too large a unit for practical use. For example, two charges of 1 C each, located in a vacuum at a distance of 100 m from each other, repel with the force

For comparison: with such force a body of mass presses on the ground

This is approximately the weight of a freight railway car, for example, with coal.

Principle of field superposition

The principle of superposition is a statement according to which the resulting effect of a complex process of influence is the sum of the effects caused by each influence separately, provided that the latter do not mutually influence each other (Physical Encyclopedic Dictionary, Moscow, “Soviet Encyclopedia”, 1983, pp. 731). It has been experimentally established that the principle of superposition is valid for the electromagnetic interaction considered here.

In the case of interaction of charged bodies, the principle of superposition manifests itself as follows: the force with which a given system of charges acts on a certain point charge is equal to the vector sum of the forces with which each of the charges in the system acts on it.

Let's explain this with a simple example. Let there be two charged bodies acting on a third body with forces and respectively. Then the system of these two bodies - the first and the second - acts on the third body with a force

This rule is true for any charged bodies, not only for point charges. The interaction forces between two arbitrary systems of point charges are calculated in Appendix 1 at the end of this chapter.

It follows that the electric field of a system of charges is determined by the vector sum of the field strengths created by the individual charges of the system, i.e.

The addition of electric field strengths according to the rule of vector addition expresses the so-called superposition principle(independent superposition) of electric fields. The physical meaning of this property is that the electrostatic field is created only by charges at rest. This means that the fields of different charges “do not interfere” with each other, and therefore the total field of a system of charges can be calculated as a vector sum of the fields from each of them separately.

Since the elementary charge is very small, and macroscopic bodies contain a very large number of elementary charges, the distribution of charges over such bodies in most cases can be considered continuous. In order to describe exactly how the charge is distributed (uniformly, non-uniformly, where there are more charges, where there are fewer, etc.) the charge throughout the body, we introduce charge densities of the following three types:

· bulk densitycharge:

Where dV- physically infinitesimal volume element;

· surface charge density:

Where dS- physically infinitesimal surface element;

· linear charge density:

where is a physically infinitesimal element of the line length.

Here everywhere is the charge of the physically infinitesimal element under consideration (volume, surface area, line segment). By a physically infinitesimal section of a body, here and below we mean a section of it that, on the one hand, is so small that under the conditions of this problem, it can be considered a material point, and, on the other hand, it is so large that it is a discrete charge (see . ratio) of this area can be neglected.

General expressions for the interaction forces between systems of continuously distributed charges are given in Appendix 2 at the end of the chapter.

Example 1. An electric charge of 50 nC is uniformly distributed over a thin rod 15 cm long. On the continuation of the axis of the rod at a distance of 10 cm from its nearest end there is a point charge of 100 nC (Fig. 1.9). Determine the force of interaction between the charged rod and the point charge.

Rice. 1.9. Interaction of a charged rod with a point charge

Solution. In this problem, the force F cannot be determined by writing Coulomb's law in the form or (1.3). In fact, what is the distance between the rod and the charge: r, r + a/2, r + a? Since, according to the conditions of the problem, we do not have the right to assume that a << r, application of Coulomb's law in its original It is impossible to formulate a formulation that is valid only for point charges; it is necessary to use a standard technique for such situations, which consists of the following.

If the force of interaction of point bodies is known (for example, Coulomb’s law) and it is necessary to find the force of interaction of extended bodies (for example, to calculate the force of interaction of two charged bodies of finite sizes), then it is necessary to divide these bodies into physically infinitesimal sections, write for each pair of such “point” » sections have a known relationship for them and, using the principle of superposition, sum (integrate) over all pairs of these sections.

It is always useful, if not necessary, to analyze the symmetry of the problem before starting to specify and perform calculations. From a practical point of view, such an analysis is useful in that, as a rule, with a sufficiently high symmetry of the problem, it sharply reduces the number of quantities that need to be calculated, since it turns out that many of them are equal to zero.

Let us divide the rod into infinitesimal segments of length , the distance from the left end of such a segment to the point charge is equal to .

The uniformity of charge distribution over the rod means that the linear charge density is constant and equal to

Therefore, the charge of the segment is equal to , from where, in accordance with Coulomb’s law, the force acting on spot charge q as a result of its interaction with point charge is equal to

As a result of interaction spot charge q at all rod, a force will act on it

Substituting numerical values ​​here, for the force modulus we obtain:

From (1.5) it is clear that when , when the rod can be considered a material point, the expression for the force of interaction between the charge and the rod, as it should be, takes the usual form of Coulomb’s law for the force of interaction between two point charges:

Example 2. A ring of radius carries a uniformly distributed charge. What is the force of interaction between the ring and a point charge q, located on the axis of the ring at a distance from its center (Fig. 1.10).

Solution. According to the condition, the charge is uniformly distributed on a ring of radius . Dividing by the circumference, we obtain the linear charge density on the ring Select an element on the ring with length . Its charge is .

Rice. 1.10. Interactions of a ring with a point charge

At the point q this element creates an electric field

We are only interested in the longitudinal component of the field, because when summing the contribution from all elements of the ring, only it is nonzero:

Integrating over, we find the electric field on the axis of the ring at a distance from its center:

From here we find the required force of interaction between the ring and the charge q:

Let's discuss the result obtained. At large distances to the ring, the value of the radius of the ring under the radical sign can be neglected, and we obtain the approximate expression

This is not surprising, since at large distances the ring looks like a point charge and the interaction force is given by the usual Coulomb law. At short distances the situation changes dramatically. Thus, when a test charge q is placed at the center of the ring, the interaction force is zero. This is also not surprising: in this case the charge q is attracted with equal force by all elements of the ring, and the action of all these forces is mutually compensated.

Since at and at the electric field is zero, somewhere at an intermediate value the electric field of the ring is maximum. Let's find this point by differentiating the expression for the tension E by distance

Equating the derivative to zero, we find the point where the field is maximum. It is equal at this point

Example 3. Two mutually perpendicular infinitely long threads carrying uniformly distributed charges with linear densities and located at a distance A from each other (Fig. 1.11). How does the force of interaction between threads depend on distance? A?

Solution. First, we will discuss the solution to this problem using the dimensional analysis method. The strength of interaction between the threads can depend on the charge densities on them, the distance between the threads and the electrical constant, that is, the required formula has the form:

where is a dimensionless constant (number). Note that due to the symmetrical arrangement of the threads, charge densities can only enter them in a symmetrical manner, in the same degrees. The dimensions of the quantities included here in SI are known:

Rice. 1.11. Interaction of two mutually perpendicular infinitely long threads

Compared to mechanics, a new quantity has appeared here - the dimension of the electric charge. Combining the two previous formulas, we obtain the equation for dimensions:

The interaction between charges occurs through an electric field. The electric field of charges at rest is called electrostatic.

Electrostatic field- a field created by electric charges that are motionless in space and constant in time (in the absence of electric currents). An electric field is a special type of matter associated with electric charges and transmitting the effects of charges on each other. The electrostatic field of a separate charge can be detected if another charge is introduced into this field, on which, in accordance with Coulomb’s law, a certain force will act.

Tension field is a vector quantity, numerically equal to the force acting on a unit positive point charge placed at a given point in the field. [E]=N/Cl=(m*kg)/(cm3*A1)=V/m. The direction of the tension vector coincides with the direction of the force. Let us determine the field strength created by a point charge q at a certain distance r from it in a vacuum; .

If different test charges q1, q2, etc. are placed at the same point, then different forces will act on them, proportional to these charges. The ratio for all charges introduced into the field will be the same and will depend only on q and r, which determine the electric field at a given point. The intensity of a given point of the electric field is the force acting on a unit positive charge placed at this point.

The unit of intensity is taken to be the intensity at a point in the field at which a unit of force acts on a unit of charge.

The principle of superposition of fields.

The result of the influence of several external forces on a particle is the vector sum of the influence of these forces.

The principle of superposition of fields, or the principle of imposition, is a convention according to which some complex process of interaction between a certain number of objects can be represented as a sum of interactions between individual objects. The principle of superposition is applicable only to those systems that are described by linear equations. Graphically, the principle of field superposition can be represented as a geometric sum of force vectors that act on a test charge placed in a field of point electric charges.

If the field is created by the simplest set of charges, which consists of positive and negative charges located at some distance from each other, then the resulting field at the observation point is found using the parallelogram rule.

The principle of superposition cannot be applied to the interaction of atoms and molecules with each other. For example, if you take two atoms whose electrons are in interaction, and bring a third similar atom to them. Some electrons from the first two atoms will be attracted and interact with the third atom. Those. the initial distribution of energy in the system will change. The initial force of interaction between the electrons and the nuclei of the first two atoms will decrease. Those. the third atom affects not only electrons, but also atomic nuclei. Also, the superposition principle cannot be applied to nonlinear systems.

Electrostatic field- a field created by electric charges that are motionless in space and constant in time (in the absence of electric currents).

An electric field is a special type of matter associated with electric charges and transmitting the effects of charges on each other.

If there is a system of charged bodies in space, then at every point of this space there is a force electric field. It is determined through the force acting on a test charge placed in this field. The test charge must be small so as not to affect the characteristics of the electrostatic field.

Electric field strength- a vector physical quantity that characterizes the electric field at a given point and is numerically equal to the ratio of the force acting on a stationary test charge placed at a given point in the field to the magnitude of this charge:

From this definition it is clear why the electric field strength is sometimes called the force characteristic of the electric field (indeed, the entire difference from the force vector acting on a charged particle is only in a constant factor).

At each point in space at a given moment in time there is its own vector value (generally speaking, it is different at different points in space), thus, this is a vector field. Formally, this is expressed in the notation

representing the electric field strength as a function of spatial coordinates (and time, since it can change with time). This field, together with the field of the magnetic induction vector, is an electromagnetic field, and the laws to which it obeys are the subject of electrodynamics.

Electric field strength in SI is measured in volts per meter [V/m] or newtons per coulomb [N/C].

The number of lines of the vector E penetrating some surface S is called the flux of the intensity vector N E .

To calculate the flux of vector E, it is necessary to divide the area S into elementary areas dS, within which the field will be uniform (Fig. 13.4).

The tension flow through such an elementary area will be equal by definition (Fig. 13.5).

where is the angle between the field line and the normal to the site dS; - projection of the area dS onto a plane perpendicular to the lines of force. Then the field strength flux through the entire surface of the site S will be equal to

Since then

where is the projection of the vector onto the normal and to the surface dS.

Superposition principle- one of the most general laws in many branches of physics. In its simplest formulation, the principle of superposition states:

the result of the influence of several external forces on a particle is the vector sum of the influence of these forces.

The most famous principle of superposition is in electrostatics, in which it states that the strength of the electrostatic field created at a given point by a system of charges is the sum of the field strengths of individual charges.

The principle of superposition can also take other formulations, which completely equivalent above:

The interaction between two particles does not change when a third particle is introduced, which also interacts with the first two.

The interaction energy of all particles in a many-particle system is simply the sum of the energies pair interactions between all possible pairs of particles. Not in the system many-particle interactions.

The equations describing the behavior of a many-particle system are linear by the number of particles.

It is the linearity of the fundamental theory in the field of physics under consideration that is the reason for the emergence of the superposition principle in it.