We will judge the magnitude of the strength or at acceleration, which force informs the body, or by the magnitude of the deformation of the body, or, finally, the magnitude of the work that the force performs when the application point is moved. To make this last method mathematically accurate and easily attributable to practical calculations, the concept of a special magnitude having the dimension of work referred to a unit of mass (or to a unit of the amount of electricity, magnetism, etc.). It is, each point of space in which the forces act is characterized by a certain potential value (t. I, p. 136). Under the potential electric field This point implies the work that is made by the field by the field when moving from this point to infinity of the unit of the number of positive electricity.

When, when moving the unit of positive electricity from this point to space, where there are no fields, the field forces really produce work, the potential at this point is positive, and it is all the greatest. So everywhere around positive chargeIf there is no nearby negative charges, the potential of the electric field is positive.

When the field forces impede the movement of a positive electricity unit from the considered point in infinity, then, it means that the work produced by them is negative and, therefore, the potential at this point is negative; In the absolute value, it is all the harder, the greater work it is necessary to spend against the forces of the field in the mentioned movement. Thus, the potential of the electric field formed by a negative charge is negative; Always negative by the potential of the field of global gravity.

If, repeating the arguments given in T. i on p.132-134, we calculated the work that the field forces were produced when moving into infinity of a positive electricity unit from a point removed from the unit point charge That we would get that this work, i.e. the potential at the specified point is:

(There is a dielectric constant environment in which the charge is

Formula (15) is easy to obtain, applying integration rules. At any point of the sphere at a distance from charge (Fig. 15), the field strength is eating when the unit of positive electricity is moved from charge to the distance in the direction of the radius, the total operation is performed equal to the integral from this value taken from

Fig. 15. To the conclusion of the formula for the potential of a point charge

Fig. 16. To the explanation of the formula of the dipole potential

When the field is formed by several (as directed) charges and the distance of a certain point on these charges, respectively, the potential at this point is equal to the algebraic amount of field potentials formed by individual charges, so (when)

The calculation shows that the potential at any point of the field formed by the dipole, at a distance from the center of the dipole (if large enough in comparison with the distance between the dipole charges) is determined by the formula

where the moment of the dipole and 6 is the angle between the direction of the axis of the dipole and the direction of the radius-vector spent from the center of the dipole in the field under consideration (Fig. 16).

It is highly important that the work of the charging in the electrostatic field, as well as the operation of moving the mass in the field, does not depend on the path of movement, and depends

only from the initial and final positions of the moved charge or mass (t. i, p. 132). For all countless trajectories, which can be carried out between points of the initial and end positions of the flow of charge, the operation of moving is the same and equal to the potential difference of these points multiplied by the moved charge:

In connection with the above, it is clear that when the transfer of the charge is returned to the starting position, i.e., when the charge is moving along a closed contour, the operation is zero.

Of the very determination of the potential as the work produced by the fields, it follows that along the power line in the positive direction of its potential decreases. The field tends to move positive electricity in the direction of the fall of the potential, and negative electricity - in the direction of increase in potential.

Since in the direction perpendicular to the power lines, charges can be moved, without spending the work (the projection of the force is equal to zero), then, therefore, the surface perpendicular to the direction of penetrating it in all its points silest linesis a surface that combines the location of the same potential. Therefore, the surface, everywhere perpendicular to the direction of power lines, is called the equipotential surface of y or, otherwise, the surface of the equal level (Fig. 17).

Note that the "drop of potential" expressions and the "surface of equal level" appeared from the analogy electrical phenomena With phenomena that can be observed during fluids. For the purpose of the form of speech, we often electricity like fluids, we say: "Electricity flows", "electric current". The potential can be like a liquid level or hydrostatic pressure. Indeed, positive electricity moves from the highest potential to the lower, as the liquid flows from the highest level to the lower.

In order for a certain amount of fluid, such as weight to raise from some level to some other level, it is necessary to spend the work of this work completely independent of the path by which we move fluid. In the same way, in the case of an electric field, the work when moving electricity from one potential does not depend on the path of movement and is expressed by a similar formula

(Click to view the scan)

As already mentioned, equipotential surface Everywhere perpendicular to the direction of the intensity vector (to the direction of power lines). Knowing the location of all equipotential surfaces (i.e. knowing the value of the potential in all points of the field), it is easy to calculate the field strength at any point. Indeed, we will imagine that through the field you are interested in the field, an equipotential surface was carried out (Fig. 18). We will spend next to the second equipotential surface where the potential for an infinitely small value is greater. Suppose that this second equipotential surface is removed from the point of the field under consideration (according to normal to the first surface) at the distance the field strength is the force acting on the point charge, equal to the unit of the amount of electricity, placed in the field under consideration, and the capacity of the potential is the work produced by the field when moving this charge; that is,

Fig. 18. To the conclusion of the formula that determines the field strength as a potential gradient:

The potential derivative along the length of movement (in the direction of normal to the surface of the level) is called the potential gradient. The potential gradient is considered as a vector directed towards the greatest increase in the potential. We see that vector of tension electrostatic field It is equal in size, and in the direction is the opposite of the electric potential gradient.

From the very potential determination, the magnitude of its unit is also followed. The absolute electrostatic unit of the potential is such a potential difference, with the passage of which one absolute electrostatic unit of the amount of electricity makes a job equal to one ERGU.

If, when moving along the normal to the surface of the level, the change in the potential occurred evenly, the field strength would be equal to the loss of the potential per 1 cm.

About tension at various points of the fields can be judged by how close to each other surface surfaces, the potentials of which differ per unit of potential. Indeed, putting in the formula we see that

Although we have introduced new concepts of the electric field and charge, so far we have been limited in essentially only by the fact that the purely Newtonian nature of forces acting between charged particles was postulated. Since the electrostatic force depends only on the distance between the two particles, this force is conservative in the sense, as it was stated in ch. 12. This allows us to introduce an extremely important concept of electrical potential energy.

FIG. 283. The difference of potential energies between points B and is equal to the one with the minus sign of the work on the movement of charge from A in

Recall that the difference in potential energies at points and is equal to the one with a sign minus the work performed above the particle when it is transferred from point A to the point (Fig. 283):

For the conservative forces, the work produced above the particle when transferring it from A B does not depend on the path (which corresponds to another

definition of conservative forces). As an example of conservative forces, we considered gravitational forces; Since the Coulomb forces are similar in shape with gravitational, they are also conservative. That is why we can introduce the concept of potential energy of charge subject to the action of forces caused by the system of other charges.

As a simple example, consider homogeneous and constant electric field E. If you multiply it for a charge, we will get the remaining strength considered in Ch. 12. We calculate the work perfect over the charged particle when it is transferred from the point A to the point as shown in FIG. 284. If the charge of the particle is positive and equal in magnitude to it will act

Then the work produced above the particle in the transition of it from A B (the distance between the points is indicated by equal to

(The work is positive, as the particle moves towards force). Thus, the difference of potential energies at points and is equal, by definition,

FIG. 284. Work performed by a particle when moving it from a in b is equal to

Often, instead of words, "I register say" grounding point b "(i.e., connect it with the Earth with the help of the conductor, as a result of which the potential energy at this point will be equal to the potential energy of the Earth, which is considered to be equal to zero); on the electrical circuits "Earth" is denoted by the symbol shown in FIG. 285.

In difficult cases, it is not always possible to simply determine the potential energy of the charge (the corresponding calculations may be extremely complex), but the calculation principle is always the same. To find the potential energy, it is necessary to calculate the work done above the charge when transferring it from one point to another, based on this distribution of charges.

By virtue of the similarity of gravitational and Coulomb forces, the electrical potential energy of charge, which is valid by the power of another charge, is similar to the gravitational potential mass of mass exposed to another mass. Recall that the gravitational potential point of point mass located at a distance from another point mass M is equal to (Fig. 286)

Similarly, the electrical potential energy of a negative point charge located at a distance from another point charge is equal to (Fig. 287)

(For convenience, the fixed point of energy countdown is considered to be located on infinity.)

A negative charge, moving from infinity to a point at a distance from a positive charge, is experiencing the strength of attraction, as well as a point mass located in the gravitational field of another mass. Therefore, electric potential energy, as well as gravitational energy, is negative. A positive charge that moved from infinity at the same point is experiencing repulsive strength, so its potential energy is the same as the energy negative chargeBut the opposite sign:

Therefore, it is convenient to introduce a new concept - the electric potential that is somewhat different from the electric potential

energy and equal to (minus) work on the movement of a single positive charge from infinity at a specified point of space. Thus, the electric potential is the potential energy divided into the charge of the injected particle. For a point positive charge, it is determined from the expression:

In some respects, it is as convenient, as the electric field: if the product of the field value at this point is determined by the power acting on this charge, the product of the magnitude of the electric potential at a given point determines the potential charge energy at this point.

In use, we, as a rule, are dealing with the differences of electrical potentials. The unit of electric potential in the SGS system is charged:

In the ISS system, the unit of electric potential - Joule / pendant, bearing the familiar name "Volt":

If the electron passes through the potential difference of 1 B, the work applied to it electric forces equal to which by definition is one electron-volt energy (work). The origin of such a unit is due to the fact that when working at accelerators, it is customary to measure the difference of electrical potentials, i.e., the usual voltage, in volts. In these machines often accelerate?

particles similar to the electron, and it turned out to be conveniently characterized by the energy that the accelerators are charged particles, the product of the voltage between the accelerator plates on the particle charge. This unit, although consists of a mixture of units of various systems, is very convenient; The fact is that its value, which is a combination of a practical unit (volt) and an electron charge, is very suitable for indicating the energy of atoms. As we will see later, with atomic reactions deal with the energies of order or J. Much is much simpler, for example, instead of trying about energy 2 eV.

work (with a minus sign), produced on charge

Electric potential

scalar value F, which is energetic. Har-Koy Elektrostatich. Fields (electric, fixed electric fields. charges). P. E. In K.L. The field of the field is equal to the attitude of the work performed by the field when the transfer will be postponed. Electric. The charge from this point to another, the potential of K-Roy is taken equal to 0, to charge. Usually believes f \u003d 0 in an infinitely remote point (in electrical engineering, it is often taken equal to 0 the potential of the Earth). P. E. - unambiguous, continuous coordinate f-ration. It is connected by S. electric field tension E and its projections on the axis of coordinate: E \u003d - Gradf, E X.= - dF / dh, e y= - dF / DU, E Z \u003d - DF / DZ. Job BUT, Performed by electrostatic. fields when transferred in it by electric. The charge is equal to the work of the charge on the difference P. E. In the initial (F 1) and the ultimate (F 2) points of the trajectory: BUT\u003d Q (F 1 - F 2). Unit P. E. (in SI) - volt(AT).

Big Encyclopedic Polytechnic Dictionary. 2004 .

Watch what is "electric potential" in other dictionaries:

Electric potential, see Electric potential ... Scientific and Technical Encyclopedic Dictionary

potential - Electric potential of this point The difference in electrical potentials of this point and another certain, arbitrarily selected point. [GOST R 52002 2003] The potential is a general term meaning the limiting possibility or the ability of some ... ...

potential - 1. In physics, the magnitude characterizing the power field is electrical, magnetic, gravitational, etc. in this point. Accordingly, the potential is electric, magnetic, etc. 2. A set of cash, opportunities in some area, ... ... Big psychological encyclopedia

POTENTIAL - Potential. The amount of any type of energy can be expressed by the product of two different quantities, from to ryy one characterizes the "energy level", determines the direction, the transition should be carried out in rum; so for example. Heavy body ... ... Big medical encyclopedia

Q, Q dimension T I ... Wikipedia

electric potential of an electrodeface layer - Electric potential of a layer. The difference of electrical potentials of a particular point on the surface of an electrodeface layer and an electrically conductive substrate or electrically conductive sublayer of an electrical image carrier. [GOST 25541 ... ... Technical translator directory

The charge number of electricity contained in the given one. Electricity. If you load into the conductive fluid, for example, into a solution of sulfuric acid, two heterogeneous metal, for example, Zn and Cu, to order these metals with each other ... ... Encyclopedia Brockhaus and Ephron

The potential of action, the type of biopotential (see bioelectric potentials) occurs on the membrane of electrically excluded cells in response to irritation by an electric field, a chemical or other incentive. At the same time, the membrane of the excitable cell ... ... encyclopedic Dictionary

POTENTIAL - (1) Piz. The value characterizing the power field (electromagnetic, gravitational, etc.) at this point; The difference P. Between the two points of the field determines the work that a test body will make (with a charge of ml. Mass equal to one) when moving ... ...

Electric potential - Phys. the value equal to the ratio of the potential energy e, which has electric charge Q, placed in this point of the electric field, to the magnitude of this charge: φ \u003d 1 ·. O. in the SI unit of electrical potential is (see) ... Large polytechnic encyclopedia

Books

• Glass electrode, Jesse Russell. This book will be made in accordance with your order using Print-On-Demand technology. High Quality Content by Wikipedia Articles! Glass electrodes - type of analytic ...
• Halvanism syndrome and chronic inflammatory processes, K. A. Lebedev, I. D. Concern. This book is devoted to the galvanism syndrome. Many aspects of this pathology until recently remained difficult to explain, and first of all its relationship with the activation of chronic ...