2.7.1. Peredomotor forces.

In electric fields on dielectrics and conductors, there are forces that call pedomotor those. (translated) forces acting on weighing Body. Term peredomotor forces certainly outdated because it was introduced at a time when existence was recognized in physics invalid substances (for example, heatborne, ether, electrical and magnetic fluids). Now it is known that weightless substances do not exist, but this term is still used. Mechanical phenomena, such as stretching the charged surface, mechanical stresses in dielectric layers, pulling the dielectric into the capacitor, the interaction of conductors with a current, the mechanical action of optical radiation on the bodies is explained by the ponderomotive forces. The nature of these forces is quite defined - they occur when exposed electromagnetic field on the electric charges.

Consider the occurrence and effect of ponderomotor forces in relation to electrostatics.

Since the electrostatic field is potentially, then for any system of electrical charges you can record

The force acting on any charge is determined, obviously, the intensity of that field in which this charge is placed (but not the field that is initiated by himself):

, (7.2)

If the charge is continuously distributed in volume with the density, then the force acting on the charge element is equal to

.

You can also enter the bulk density of forces that is equal

. (7.3)

Forces acting in polarized dielectric.

Forces acting on electric dipoles in substance deforming and orienting them in space belong to the ponderomotive forces.

Earlier in §1.7 we received expression (7.13) for the strength acting on a single dipole in the electric field. Moreover, as we found out, the force acting in a homogeneous field on a separate dipole is zero.

Consider now the forces acting in the amount of dielectric placed in electric field. The force applied to the element of the size of the dielectric is equal to the amount of forces acting on elementary dipoles within the volume under consideration:

, (7.4)

moreover, the summation is conducted on all elementary dipoles in volume. Since the volume element is small, then the vector of tension electric field - Slowly changing the value of this volume. Therefore, introducing a polarization vector, we can record

From here the bulk density of forces in the dielectric:

. (7.6)

For homogeneous dielectric ratio

,

then we get an expression for the bulk density of forces in the form:

. (7.7)

We use the identity of the vector algebra (see (7.12), §1.7),

Recorded for:

. (7.8)

Since for the electrostatic field, we now receive for the volumetric density of the ponderomotive forces:

. (7.9)

If a homogeneous dielectric in question (,), then

. (7.10)

Formulas (7.9) and (7.10), expressing the volumetric density of the forces are valid both for absolutely hard and elastically deformable dielectrics. The last statement is valid only if the polarization of the dielectric (polarization vector) is linearly dependent on its mass, i.e. The dipole moments of molecules and atoms during compression and stretching of the volume element do not change.

If a the dielectric constant Not constant, and we are dealing with compressible dielectrics, the definition of ponderomotor forces is quite difficult. The general method for calculating ponderomotor forces gives thermodynamics - thermodynamics of dielectrics. Thermodynamic functions of dielectrics are determined - free energy, thermodynamic potential, enthalpy. In this course, we will not do it.

2.7.2. Forces acting on surface charges.

Earlier, we have already affected this issue. If there is a closed conductive surface charged with surface density, the electric field is known on both sides, and , and on the surface itself, the electric field is not defined. As a result of the interaction of surface charges, the conductor surface is stretched. How to find power acting per unit surface?

Consider a secluded conductor. We highlight the surface element:

1) the field from the outer side of the selected surface element is equal;

2) Field inside.

The field inside and outside the conductor can be considered as a superposition of fields created by the surface element itself, i.e. , and all other charges that are on the surface :. The field is equally large on both sides of the site, but has opposite directions. The field is equally module and the direction above and under the site.

In the SI coefficient of proportionality in the law of the coulon is equal

k \u003d 9 · 10 9 N · m 2 / CL 2.

According to the Coulomb law, two point charges of 1 CL, located in a vacuum at a distance of 1 m from each other, interact with force F.= 9 · 10 9 H, approximately equal to the weight of the Egyptian pyramids. It is clear from this assessment that the pendant is a very large unit of charge. In practice, therefore, the dolly units of the coulon usually use.

The previously discussed law covers the quantitative and qualitative features of the interaction of point electrical charges in vacuo. However, this law does not answer a very important question about the mechanism of charge interaction, i.e. Through which the action of one charge on another is transmitted. The search for the answer to this question has led English physics M. Faraday To the hypothesis about the existence of an electric field, the justice of which was fully confirmed by subsequent studies. According to the idea of \u200b\u200bFaraday, electrical charges do not act on each other directly. Each of them creates an electric field in the surrounding space. The field of one charge acts on another charge, and vice versa.

All of the above allows you to give the following definition:

electric field - This is a special kind of matter, through which electrical charges are interacted.

Electric field properties

Electric field material. exists regardless of our knowledge about him.

An electrical charge is generated: There is an electric field around any charged body.

The field created by stationary electric charges is called electrostatic .

The electrical field can be created and variable magnetic field. Such an electric field is called vikhrev .

Electric field distributed by in space S. ultimate speedequal to the speed of light in vacuum.

Electric field effect on electric charges

The electric field can be viewed as mathematical modeldescribing the value of the magnitude tension Electric field at this point of space.

The electric field is one of the components united electromagnetic fieldand manifestation of electromagnetic interaction

We must enter quantitative characteristic of the field. After that, the electrical fields can be compared with each other and continue to study their properties.

To study the electric field we will use trial charge: under trial charge We will understand the positive point charge, which does not change the studied electrical field .

Let the electrical field be created by a point charge Q 0. If you make a test charge Q 1 in this field, force will act on it.

noteThat in this topic we use two charges: the source of the electrical field Q 0 and the test charge Q 1. The electrical field is valid only on the test charge Q 1 and cannot act on its source, i.e. On the charge Q 0.

According to the Culon law, this force is proportional to the charge Q 1:

.

Therefore, the ratio of force acting on the box is placed at this point Q 1, to this charge at any point of the field:

does not depend on the charged Q 1 and can be considered as a field characteristic. This power characteristic is called electric field tension .

Like strength, field strength - vector quantity, it is denoted by the letter.

The field strength is equal to the ratio of power with which the field acts on the point charge, to this charge.

E.which is his silence characteristic: The tension of the electrostatic field shows how power the electrostatic field acts on a single positive electrical charge placed at this point point. The direction of tension vector coincides with the direction of force acting on a positive charge, and the opposite direction of force acting on a negative charge.

The electrostatic field is stationary (constant) if its tension does not change over time. Stationary electrostatic fields Created by fixed electrical charges.

The electrostatic field is uniformly, if the vector of its intensity is the same in all points of the field, if the vector of tension at different points varies, the field is inhomogeneous. Uniform electrostatic fields are, for example, electrostatic fields of a uniformly charged finite plane and a flat capacitor far from the edges of its plates.

One of the fundamental properties of the electrostatic field is that the operation of the power of the electrostatic field when the charge is moved from one point of the field to another does not depend on the trajectory of the movement, but is determined only by the position of the initial and endpoint and the charge values. Consequently, the work of the power of the electrostatic field when the charge is moving along any closed trajectory is zero. Power fieldsWith this property, is called potential or conservative. That is, the electrostatic field is a potential field, energy characteristic which is the electrostatic potential associated with the vector of tension E. By the ratio:

E \u003d -GradJ..

For graphic image The electrostatic fields use power lines (intensity lines) - imaginary lines, tangents to which coincide with the direction of the tension vector at each point.

For electrostatic fields, the principle of superposition is observed. Each electrical charge creates an electric field in space, regardless of the presence of other electrical charges. The tension of the resulting field created by the charge system is equal to the geometric sum of the field strengths created at this point each of the charges separately.

Any charge in the surrounding space creates an electrostatic field. To detect the field at any point, you need to put a point test charge to the observation point - a charge that does not distort the field under study (no redistribution of charges that create the field).

The field created by a secluded point charge q.is spherically symmetrical. The intensity module of a secluded point charge in vacuo with the help of the Culon law can be represented as:

E \u003d Q / 4PE about R 2.

Where E o is electrical constant, \u003d 8.85. 10 -12 f / m.

The law of the coulon, established with the help of the tweeted scales created by it (see Cut Scales), is one of the main laws describing the electrostatic field. It establishes the relationship between the strength of the interaction of charges and the distance between them: the strength of the interaction of two point fixed charged bodies in a vacuum is directly proportional to the product of charge modules and inversely proportional to the square square between them.

This force is called Coulomb, and the field is Coulomb. In the Coulomb field, the direction of the vector depends on the charge sign Q: If q\u003e 0, then the vector is directed along the radius from charge if Q? Once (? - dielectric permeability of the medium) less than in vacuum.

The experimentally established law of the coulon and the principle of superposition allow you to fully describe the electrostatic field of a given charge system in vacuo. However, the properties of the electrostatic field can be expressed in another, more general form, without resorting to the submission of the Coulomb field of the point charge. The electric field can be characterized by the value of the stream of the electric field intensity, which can be calculated in accordance with the Gauss Theorem. The Gaussian Theorem establishes the relationship between the stream of electric field strength through a closed surface and charge inside this surface. The stream of tension depends on the field distribution over the surface of one or another area and is proportional to the electrical charge within this surface.

If an insulated conductor is placed in an electric field, then on free charges q. The power will act in the conductor. As a result, a short-term movement of free charges arises in the conductor. This process will end when the own electrical field of charges arising on the surface of the conductor compensates completely external field, i.e. the equilibrium distribution of charges will be established, in which the electrostatic field inside the conductor appeals to zero: at all points inside the conductor E. \u003d 0, that is, there is no field. The power lines of the electrostatic field outside the conductor in the immediate vicinity of its surface are perpendicular to the surface. If it were not so, then there would be a field strength of the field, along the surface of the conductor and the current would occur over the surface. Charges are located only on the surface of the conductor, while all the surface points of the conductor have the same potential value. The surface of the conductor is an equipotential surface. If there is a cavity in the conductor, the electric field in it is also zero; This found electrostatic protection of electrical appliances.

If a dielectric is placed in an electrostatic field, then the polarization process occurs - the process of orientation of dipoles or the appearance under the influence of the electric field oriented by the field of dipoles. In a homogeneous dielectric, the electrostatic field due to polarization (see Polarization of dielectrics ) decrease in? time.

LECTURE NOTES

ELECTROSTATICS

Lecture 1.

Basics of electrostatics

Electrostatics in vacuum

ELECTRIC CHARGE

Electric, or electrostatic interaction is one of the fundamental types of interaction considered in physics. Electric power There are, for example, between electrons and protons, as well as between electrons. These forces are significantly more gravitational, and are generated by electric charges.

The first information about electricity belongs to electrical charges obtained by friction. The electrical chains entering the current to the light bulbs and electric motors appeared with the invention of the batteries after 1800. In 1752-53g. Lomonosov and Richman in Russia and Franklin in America proved the general nature of atmospheric electricity and electrification by friction. Powerful lightning and weak sparks observed when combing hair comb, is electrical discharges in the air, differing only in the scale of the phenomenon.

The initial for all electrodynamics are such concepts as "Electric charge" and "electromagnetic field". The concept of "electrical charge" is closely related to the special properties of charged bodies and particles, which are manifested in the formation of an electromagnetic field, accompanying charge, and in the power action of the field for charge. These two different properties of charged bodies - to create a field and experience the action of the field of other charges - are characterized by the same value - electrical charge q.

The amount of charge is determined in physical dimensions for one or another manifestations of electromagnetic interaction. Thus, for point resting charges, it is assumed that the strength of the interaction between them is proportional to the magnitude of the charges (the law of Culon). Therefore, choosing a single charge, you can determine the value of another charge, comparing the strengths of the interaction of charges: a single one and a single one with an unknown.

The unit of charge measurement is pendant (CL).

Charge - the value is scalar and is expressed by valid numbers: may have positive, zero and negative values. The magnitude of the charge is invariant to Lorentz transforms, i.e. The charge of some body or particle is expressed in the same number in all inertial reference systems. Finally, the charge is an additive value: when connecting several spot charges In one "resulting" charge is equal to the algebraic amount of the connected charges. The charge of any system of charged bodies and particles is equal to the sum of charges of individual bodies and particles. The charge of the macroscopic body is equal to the sum of charges of its parts.

Electric charge by nature is discretened. The limit of the electric charge is an elementary charge inherent in electrons, protons and other elementary particles, its module e.\u003d 1,6021892 · 10 CL.

Sub-elementary particles - quarks - have charges ± e /3 or ± 2 e /3, but they are not observed in free state.

In classical electrodynamics, macroscopic charges are considered, which are considered continuous, and continuous charges can be considered only without taking into account the existence of the smallest elementary charge. It follows that the concept of infinitely small charge dQ. It has a physical, and not literally mathematical meaning: dQ. Little in comparison with some full charge q., but still so great compared to the elementary charge, that the discreteness of elementary charges can not be taken into account.

The continuity of the electrical charge allows and continuously distributed along the line, surface, in space. This distribution is described by the charge density. If the charge is distributed over a certain line, then they talk about linear density:

when the charge distribution over the surface is introduced surface density

if the charge is located in some area of \u200b\u200bspace, its distribution is described by bulk density

The concept of "point charge" in classical electrodynamics can be given a two-way meaning. First, an infinitely small charge is accepted for the spot charge dQ., located in an infinitely small volume of space. This model of point charge corresponds to its continuous distribution in space, in this case dQ \u003d ρDV.Secondly, in many cases a model of discrete in the space of a point charge, when a macroscopic charge q. Any magnitude is placed in a geometric point of space.

Elementary Electric Electric Charge e. Also is point. But as for the discrete charge charges of elementary particles, then within the framework of classical electrodynamics, there is no possibility to raise the question of the characteristics introduced into the electromagnetic interaction of the discreteness of charges both in size and by spatial distribution. The interactions of elementary charges between themselves are described by quantum electrodynamics.

The law of conservation of electrical charges is the fundamental law of physics along with the laws of energy conservation, pulse and moment of impulse. According to this law with any known interactions of elementary particles among themselves, the algebraic amount of electrical charges of particles to the interaction is equal to the amount of electrical charges of particles after interaction. At the same time, particles are not preserved as such, they are not preserved and their total numberSince some particles disappear, while others appear.

Classical electrodynamics studies the processes at which there are no mutual transformations of charged particles, so the law of saving charge here is a simple effect of preserving its carriers - electrons and protons. In an isolated system, the electrical charge is saved.

With the electrification of bodies, friction always contains both bodies, and one of them receives a positive charge, and the other is the same largest charge, if it is electrically neutral before the body interaction. Thus, electrical charges do not occur and do not disappear, they can only be transmitted from one body to another or moved inside this body. In any neutral substance there are charges of both signs in equal amounts, and as a result of contacting the two bodies, part of the charges passes from one body to another. Equality of the amount of positive and negative charges in each body is violated, and they charge variemen.

The law of Kulon.

The main law of interaction of electrical charges was found by Charlock Pendant in 1785. Experimentally. Pendant found that the strength of the interaction between two small charged metal balls is inversely proportional to the square of the distance between them and depends on the values \u200b\u200bof charges and:

where is the proportionality coefficient. Forces acting on charges are central, that is, they are directed along a straight line connecting charges. For the same charges, the work and force corresponds to the mutual repulsion of charges, for varieme charges, and the force corresponds to the mutual attraction of charges.

The law of the coulon can be written in vector form:

,

where is the vector of force acting on the charge from the charge,

Radius vector connecting charge with charge; - Module radius-vector.

The force acting on the charge from the side is equal

, .

Forces acting on charges are central and directed in a straight line connecting charges (Fig.1.1.1).

The law of the coulon in this form is valid only for the interaction of point electrical charges, that is, such charged bodies, the linear dimensions of which can be neglected compared with the distance between them. In addition, it expresses the power of interaction between fixed electrical charges, that is, this is an electrostatic law.

Formulation of the Law of Cool:

The power of electrostatic interaction between two point electric charges is directly proportional to the product values \u200b\u200bof charges, inversely proportional to the square of the distance between them, and directed in a straight line connecting charges.

The coefficient of proportionality in the law of the coulon depends on the properties of the medium and the choice of units of measurement of the values \u200b\u200bincluded in the formula. Therefore, you can imagine the relationship

where - the coefficient depending only on the choice of system of units of measurement; - a dimensionless value that characterizes the electrical properties of the medium is called the relative dielectric permeability of the medium. It does not depend on the choice of the system of units of measurement and is equal to one in vacuo.

Then the law of Kulon will take the form:

for vacuum, then - the relative dielectric permeability of the medium shows how many times in this medium the power of the interaction between two point electrical charges and, which are from each other at a distance, less than in vacuum.

In the system of the coefficient, and the law of the coulon has the form:

.

This is rationalized record of the Culon law. Here - electric constant ,.

In vector form, the law of the coulon takes where - the vector of force acting on the charge from the charge - a radius-vector spent from charge to charge (Fig.1.1.2), r. - Module radius-vector.

Any charged body consists of a variety of point electrical charges, so electrostatic force with which one charged body acts to another is equal to the vector sum of the forces applied to all point charges of the second body from each point charge of the first body.

ELECTRIC FIELD. Electrostatic field tension

The space in which the electrical charge is located has certain physical properties. On any other the charge introduced into this space is operated by the electrostatic forces of the coulon. If at each point is the strength, it is said that in this space there is a power field. The field along with the substance is a form of matter. If the field is stationary, that is, does not change in time, and is created by fixed electrical charges, then such a field is called electrostatic. Elektrostatics studies only electrostatic fields and interactions of fixed charges.

The concept of tension is introduced for the characteristics of the electric field. The tension at each point of the electric field is called the vector, numerically equal to the ratio of the force with which this field acts on a test positive charge, placed at this point, and the values \u200b\u200bof this charge, and directed towards the action of force.

A trial charge that is entered in the field is assumed point. It does not participate in the creation of a field that is measured with it. In addition, it is assumed that this charge does not distort the fields under study, that is, it is small enough and does not cause the redistribution of charges that create the field.

If the field is valid for a test point, then tensions

Units of tension in the SI N / CL \u003d V / m.

Expression for the strength of the point charge field:

.

In vector form:

Here - a radius-vector spent from charge q. creating a field at this point.

Thus, vectors of the electric field of point charge q. At all points, the fields are directed radially from charge if it is positive (Fig.1.1.3), and to the charge, if he is negative (Fig.1.1.3).

For the graphical interpretation of the electric field, the concept of a power line is introduced or thread lines. it curve, tangential at each point to which coincides with the vector of tension. The line of tension begins on a positive charge and ends on a negative. The line of tension does not intersect, since at each point of the field, the vector of tension has only one direction.

Electrification tel

Electrification - The phenomenon of accumulation of an electric charge. No less than two bodies are always involved in electrification. For the flow of the phenomenon between bodies, close contact is necessary. Sometimes this contact is achieved at the expense of friction between the bodies, which leads to an erroneous opinion on the need for friction or carrying out work on electrification tel. The electrification phenomenon is explained through the movement of free charges (electrons).

There are several methods of electrification.

1. Electric friction. At the same time, two previously uncharged bodies made from different substances are used. In the process of electrification, the charge accumulate both bodies, one - positive, the other is negative and equal to the first body charge module (the law of saving charge). From the point of view of molecular-kinetic theory, with electrification by friction, the substance with a stronger interaction captures electrons in the second substance and accumulates a negative charge.

2. Electrification contact. In this case, several bodies can participate, which are capable of carrying out electrical charges. To contact one or more bodies possessed electric charges. After contacting the charges redistributed in proportion to the electric capacity of the tel.

3. Electrification electrostatic induction (See "Conductors in an electric field").

The interaction of charges. Two types of charge

Electric charge - Main scalar physical quantitydetermining the intensity of electromagnetic interactions. It is said that the body has an electric charge if the forces of electrical or magnetic nature are detected with other bodies. The unit of electrical charge is introduced through the current force unit.

[q.] \u003d CL \u003d A ∙ s.

1 CL - This is a charge passing through a cross-section of the conductor at a current of 1 and for 1 s.

Consider the electrical charge properties obtained experimentally.

1. There are two types of electrical charges. Positive They call the charge of the glass stick, obtained by it when electrifying friction about Silk. A positive charge is a lack of electrons. Negative They call the charge of an ebony stick, obtained by it when electrifying friction about wool (fur). Negative charge - It is an excess of electrons in the body.

2. The charges of the same name are repelled, obtained are attracted. The interaction forces of point charges are directed along the straight, which connects them. The magnitude of the interaction is described in the law of the coulon.

3. There is a limit of the delicacy of an electric charge. Elementary Call the minimum (indivisible) electrical body charge. Elementary particle with a positive elementary charge - proton, negative - electron. The value of the elementary charge is a fundamental physical constant: e. \u003d 1.6 ∙ 10 -19 CB.

Electric charge discrete: | q.| = Ne.

Electrical charge has a property of saving.

To detect charges is used electroscope.

Electric charge conservation law

One of the main properties of the electric charge is its ability to save. The law of maintaining an electric charge: in an electrically isolated system, the algebraic amount of electrical charges of all bodies included in this system remains constant.

Electrically isolated system - System, across the border of which there is no charge transfer in any direction.

The law of Kulon.

The law of interaction of electric charges was established by the experimentally French physicist Sh. Pendant in the second half of the XVIII century. The law is formulated as follows: the module of the interaction force of two fixed point charges is directly proportional to the product of the modules of these charges and inversely proportional to the square of the distance between them.

For vacuum and air, the law of Kulon is recorded like this:

where k. - proportionality coefficient, depending on the choice of units. In S.

where – electric constant.

For an infinite homogeneous and isotropic dielectric environment, the law of Kulon has the form:

where ε is the dielectric permeability of the medium in which there are charges.

The law of the coulon is fair for spot charges - charged bodies whose dimensions are much less than other sizes of the system under consideration. If the charged body in the conditions of this task cannot be considered a point charge, then it is considered as a set of point charges. The force with which such a body will act on another body is determined according to the principle of superposition of forces.

Electric field effect on electric charges

To describe the interaction of electrical charges at the beginning of the XIX century, the English physicist M. Faraday proposed to use the concept of an electric field.

Electric field - Material medium, which is an intermediary of a single charge to another and transmitting this action at a final rate.

The idea of \u200b\u200bFaraday: any electric charge creates a material object in all surrounding its space - electric fieldwhich acts on other electrical charges with some force called electrical power , and decreases as it removed from charge, creating it.

The charge gives the surrounding space by special physical properties, most importantly of which is an effect with electrical power on any charge placed in this space.

The field created by fixed electrical charges does not change over time and is called electrostatic.

Electric fields are taken graphically using silest lines - lines tangents to which at any point coincide with the direction of the voltage vector at this point. Graphic Pollution of Electric Fields is given in compliance with the following rules:

1) power lines electric field start on positive charges and ends on negative;

2) the power lines do not intersect;

3) The lines density is proportional to the voltage vector module in this field location.

The figures contain several examples of graphic fields of fields.