Force lines of the electrostatic field. Electric field lines

For a visual graphical representation of the field, it is convenient to use lines of force - directed lines, the tangents to which at each point coincide with the direction of the electric field strength vector (Fig. 233).

Rice. 233
According to the definition, the lines of force of the electric field have a series common properties(compare with properties of fluid streamlines):
 1. lines of force do not intersect (otherwise, two tangents can be constructed at the intersection point, that is, at one point, the field strength has two values, which is absurd).
2. The lines of force do not have kinks (at the kink point, again, you can build two tangents).
3. The lines of force of the electrostatic field begin and end on charges.
Since the field strength is determined at each spatial point, then the line of force can be drawn through any spatial point. Therefore, the number of lines of force is infinitely large. The number of lines that are used to depict the field is most often determined by the artistic taste of the physicist-artist. In some teaching aids it is recommended to build a picture of field lines so that their density is greater where the field strength is greater. This requirement is not strict, and not always feasible, so the lines of force are drawn, satisfying the formulated properties 1 − 3 .
It is very easy to plot the lines of force of the field created by a point charge. In this case, the lines of force are a set of straight lines emerging (for positive) or entering (for negative) at the charge location point (Fig. 234).

rice. 234
Such families of force lines of the fields of point charges demonstrate that the charges are the sources of the field, by analogy with the sources and sinks of the fluid velocity field. We will prove later that lines of force cannot begin or end at points where there are no charges.
The picture of field lines of real fields can be reproduced experimentally.
Pour a small layer into a low vessel castor oil and pour a small portion of semolina into it. If oil with cereals is placed in an electrostatic field, then grains of semolina (they have a slightly elongated shape) turn in the direction of the electric field strength and line up approximately along the lines of force, after a few tens of seconds, a picture of the lines of force of the electric field emerges in the cup. Some of these "pictures" are presented in photographs.
It is also possible to carry out a theoretical calculation and construction of force lines. True, these calculations require an enormous number of calculations, so it is realistic (and without special work) are carried out using a computer, most often such constructions are performed in a certain plane.
When developing algorithms for calculating the pattern of field lines, a number of problems are encountered that need to be resolved. The first such problem is the calculation of the field vector. In the case of electrostatic fields created by a given charge distribution, this problem is solved using Coulomb's law and the principle of superposition. The second problem is the method of constructing a separate line. The idea of ​​the simplest algorithm that solves this problem is quite obvious. In a small area, each line practically coincides with its tangent, so you should build a lot of segments tangent to the lines of force, that is, segments of small length l, the direction of which coincides with the direction of the field at a given point. To do this, it is necessary, first of all, to calculate the components of the intensity vector in given point E x, E y and the modulus of this vector E = √(E x 2 + E y 2 ). Then you can build a segment of small length, the direction of which coincides with the direction of the field strength vector. its projections on the coordinate axes are calculated by the formulas that follow from Fig. 235:

rice. 235

Then you should repeat the procedure, starting from the end of the constructed segment. Of course, when implementing such an algorithm, there are other problems that are more of a technical nature.
Figures 236 show the lines of force of the fields created by two point charges.


rice. 236
The signs of the charges are indicated, in figures a) and b) the charges are the same in modulus, in fig. c), d) are different - which of them we propose to determine more independently. In each case, also determine the directions of the lines of force yourself.
It is interesting to note that M. Faraday considered the lines of force of the electric field as real elastic tubes interconnecting electric charges, such representations helped him a lot to predict and explain many physical phenomena.
Agree that the great M. Faraday was right - if you mentally replace the lines with elastic rubber bands, the nature of the interaction is very clear.

The Ostrogradsky–Gauss theorem, which we will prove and discuss later, establishes a connection between electric charges and electric field. It is a more general and more elegant formulation of Coulomb's law.

In principle, the strength of the electrostatic field created by a given charge distribution can always be calculated using Coulomb's law. The total electric field at any point is the vector sum (integral) contribution of all charges, i.e.

However, with the exception of the most simple cases, it is extremely difficult to calculate this sum or integral.

Here the Ostrogradsky-Gauss theorem comes to the rescue, with the help of which it is much easier to calculate the electric field strength created by a given charge distribution.

The main value of the Ostrogradsky-Gauss theorem is that it allows deeper understanding of the nature of the electrostatic field and establishes more general relation between charge and field.

But before moving on to the Ostrogradsky-Gauss theorem, it is necessary to introduce the concepts: lines of force electrostatic field and tension vector flow electrostatic field.

In order to describe the electric field, you need to set the intensity vector at each point of the field. This can be done analytically or graphically. For this they use lines of force- these are lines, the tangent to which at any point of the field coincides with the direction of the intensity vector(Fig. 2.1).

Rice. 2.1

The line of force is assigned a certain direction - from a positive charge to a negative one, or to infinity.

Consider the case uniform electric field.

Homogeneous called an electrostatic field, at all points of which the intensity is the same in magnitude and direction, i.e. A uniform electrostatic field is depicted by parallel lines of force at an equal distance from each other (such a field exists, for example, between the plates of a capacitor) (Fig. 2.2).

In the case of a point charge, the lines of tension emanate from the positive charge and go to infinity; and from infinity enter into a negative charge. Because then the density of field lines is inversely proportional to the square of the distance from the charge. Because the surface area of ​​the sphere through which these lines pass itself increases in proportion to the square of the distance, then total number lines remains constant at any distance from the charge.

For a system of charges, as we see, the lines of force are directed from a positive charge to a negative one (Fig. 2.2).

Rice. 2.2

Figure 2.3 also shows that the density of field lines can serve as an indicator of the value.

The density of field lines should be such that a unit area normal to the intensity vector is crossed by such a number that is equal to the modulus of the intensity vector, i.e.

In the space surrounding the charge that is the source, is directly proportional to the amount of this charge and inversely to the square of the distance from this charge. The direction of the electric field according to the accepted rules is always from a positive charge towards a negative charge. This can be represented as if a test charge is placed in the space region of the electric field of the source and this test charge will either repel or attract (depending on the sign of the charge). The electric field is characterized by strength , which, being a vector quantity, can be represented graphically as an arrow having a length and direction. Anywhere the direction of the arrow indicates the direction of the electric field strength E, or simply - the direction of the field, and the length of the arrow is proportional to the numerical value of the electric field strength in this place. The farther the region of space is from the source of the field (charge Q), the smaller the length of the intensity vector. Moreover, the length of the vector decreases with distance to n times from some place in n 2 times, that is, inversely proportional to the square.

A more useful means of visualizing the vector nature of an electric field is to use such a concept as, or simply, lines of force. Instead of depicting countless vector arrows in space surrounding the source charge, it turned out to be useful to combine them into lines, where the vectors themselves are tangent to points on such lines.

As a result, successfully used to represent the vector picture of the electric field electric field lines, which leave the charges of a positive sign and enter the charges negative sign, and also extend to infinity in space. This representation allows you to see with the mind the electric field invisible to the human eye. However, this representation is also convenient for gravitational forces and any other contactless long-range interactions.

The model of electric field lines includes an infinite number of them, but too high a density of the image of field lines reduces the ability to read field patterns, so their number is limited by readability.

Rules for drawing electric field lines

There are many rules for compiling such models of electrical power lines. All these rules are designed to provide the most information when visualizing (drawing) an electric field. One way is to depict field lines. One of the most common ways is to surround more charged objects. large quantity lines, that is, a greater density of lines. Objects with a large charge create stronger electric fields and therefore the density (density) of lines around them is greater. The closer to the charge the source, the higher the density of field lines, and the greater the charge, the thicker the lines around it.

The second rule for drawing electric field lines involves drawing lines of a different type, such as those that intersect the first lines of force. perpendicular. This type of line is called equipotential lines, and in the case of a volumetric representation, one should speak of equipotential surfaces. This type of line forms closed contours and each point on such an equipotential line has same value field potential. When any charged particle crosses such perpendicular lines of force lines (surfaces), then they talk about the work done by the charge. If the charge moves along equipotential lines (surfaces), then although it moves, no work is done. A charged particle in electric field another charge begins to move, but in static electricity only stationary charges are considered. The movement of charges is called electric shock, while work can be done by the charge carrier.

It is important to remember that electric field lines do not intersect, and lines of another type - equipotential, form closed loops. In the place where there is an intersection of two types of lines, the tangents to these lines are mutually perpendicular. Thus, something like a curved coordinate grid, or a lattice, is obtained, the cells of which, as well as the points of intersection of the lines different types characterize the electric field.

Dashed lines are equipotential. Lines with arrows - electric field lines

Electric field consisting of two or more charges

For solitary individual charges electric field lines represent radial rays emerging from charges and going to infinity. What will be the configuration of field lines for two or more charges? To perform such a pattern, it must be remembered that we are dealing with a vector field, that is, with electric field strength vectors. To depict the field pattern, we need to perform the addition of the intensity vectors from two or more charges. The resulting vectors will represent the total field of several charges. How can lines of force be drawn in this case? It is important to remember that each point on the field line is single point contact with the electric field strength vector. This follows from the definition of a tangent in geometry. If from the beginning of each vector we construct a perpendicular in the form of long lines, then the mutual intersection of many such lines will depict the very desired line of force.

For a more accurate mathematical algebraic representation of the lines of force, it is necessary to compose the equations of the lines of force, and the vectors in this case will represent the first derivatives, the lines of the first order, which are the tangents. Such a task is sometimes extremely complex and requires computer calculations.

First of all, it is important to remember that the electric field from many charges is represented by the sum of the intensity vectors from each charge source. This is the basis to perform the construction of field lines in order to visualize the electric field.

Each charge introduced into the electric field leads to a change, even if insignificant, in the pattern of field lines. Such images are sometimes very attractive.

Electric field lines as a way to help the mind see reality

The concept of an electric field arose when scientists tried to explain the long-range action that occurs between charged objects. The concept of an electric field was first introduced by the 19th century physicist Michael Faraday. It was the result of Michael Faraday's perception invisible reality in the form of a picture of lines of force characterizing long-range action. Faraday did not think within the framework of one charge, but went further and expanded the boundaries of the mind. He suggested that a charged object (or mass in the case of gravity) affects space and introduced the concept of a field of such influence. Considering such fields, he was able to explain the behavior of charges and thereby revealed many of the secrets of electricity.

There are scalar and vector fields (in our case, the vector field will be electric). Accordingly, they are modeled by scalar or vector functions of coordinates, as well as time.

The scalar field is described by a function of the form φ. Such fields can be visualized using surfaces of the same level: φ (x, y, z) = c, c = const.

Let us define a vector that is directed towards the maximum growth of the function φ.

The absolute value of this vector determines the rate of change of the function φ.

Obviously, a scalar field generates a vector field.

Such an electric field is called potential, and the function φ is called potential. Surfaces of the same level are called equipotential surfaces. For example, consider an electric field.

For a visual display of the fields, the so-called electric field lines are built. They are also called vector lines. These are lines whose tangent at a point indicates the direction of the electric field. The number of lines that pass through the unit surface is proportional to the absolute value of the vector.

Let us introduce the concept of a vector differential along some line l. This vector is directed tangentially to the line l and is equal in absolute value to the differential dl.

Let some electric field be given, which must be represented as field lines of force. In other words, let's define the coefficient of stretching (compression) k of the vector so that it coincides with the differential. Equating the components of the differential and the vector, we obtain a system of equations. After integration it is possible to construct the equation of force lines.

In vector analysis, there are operations that provide information about which electric field lines are present in a particular case. Let us introduce the concept of “vector flow” on the surface S. The formal definition of the flow Ф has the following form: the quantity is considered as the product of the usual differential ds by the unit vector of the normal to the surface s. The unit vector is chosen so that it defines the outer normal of the surface.

It is possible to draw an analogy between the concept of a field flow and a substance flow: a substance per unit time passes through a surface, which in turn is perpendicular to the direction of the field flow. If the lines of force go out of the surface S, then the flow is positive, and if they do not go out, then it is negative. In general, the flow can be estimated by the number of lines of force that come out of the surface. On the other hand, the magnitude of the flux is proportional to the number of field lines penetrating the surface element.

The divergence of the vector function is calculated at the point whose band is the volume ΔV. S is the surface covering the volume ΔV. The divergence operation makes it possible to characterize points in space for the presence of field sources in it. When the surface S is compressed to the point P, the electric field lines penetrating the surface will remain in the same quantity. If a point in space is not a field source (leakage or sink), then when the surface is compressed to this point, the sum of field lines, starting from a certain moment, equals zero (the number of lines entering the surface S is equal to the number of lines emanating from this surface).

The closed loop integral L in the definition of the rotor operation is called the circulation of electricity along the loop L. The rotor operation characterizes the field at a point in space. The direction of the rotor determines the magnitude of the closed field flow around a given point (the rotor characterizes the field vortex) and its direction. Based on the definition of the rotor, by simple transformations, it is possible to calculate the projections of the electricity vector in the Cartesian coordinate system, as well as the electric field lines.

ELECTROSTATIC FIELD

electrostatic field trial charge q0

tension

, (4)

, . (5)

lines of force

THE WORK OF THE FORCES OF THE ELECTROSTATIC FIELD. POTENTIAL

An electric field, like a gravitational one, is potential. Those. the work performed by electrostatic forces does not depend on which route the charge q is moved in the electric field from point 1 to point 2. This work is equal to the difference in potential energies that the moved charge has at the initial and final points of the field:

A 1,2 \u003d W 1 - W 2. (7)

It can be shown that the potential energy of a charge q is directly proportional to the magnitude of this charge. Therefore, as the energy characteristic of the electrostatic field, the ratio of the potential energy of a test charge q 0 placed at any point of the field to the value of this charge is used:

This value is the amount of potential energy per unit of positive charge and is called field potential at a given point. [φ] = J / C = V (Volt).

If we assume that when the charge q 0 is removed to infinity (r → ∞), its potential energy in the field of charge q vanishes, then the potential of the field of a point charge q at a distance r from it:

. (9)

If the field is created by a system of point charges, then the potential of the resulting field is equal to the algebraic (including signs) sum of the potentials of each of them:

. (10)

From the definition of potential (8) and expression (7), the work done by the forces of the electrostatic field to move the charge from

point 1 to point 2 can be represented as:

ELECTRIC CURRENT IN GASES

NON-SELF GAS DISCHARGE

Gases at not too high temperatures and at pressures close to atmospheric are good insulators. If placed in a dry atmospheric air, a charged electrometer, then its charge remains unchanged for a long time. This is explained by the fact that gases under normal conditions consist of neutral atoms and molecules and do not contain free charges (electrons and ions). A gas becomes a conductor of electricity only when some of its molecules are ionized. For ionization, the gas must be exposed to some kind of ionizer: for example, an electric discharge, x-rays, radiation or UV radiation, candle flame, etc. (in the latter case, the electrical conductivity of the gas is caused by heating).

When gases are ionized, they escape from the external electron shell an atom or molecule of one or more electrons, resulting in free electrons and positive ions. Electrons can attach to neutral molecules and atoms, turning them into negative ions. Therefore, in an ionized gas there are positively and negatively charged ions and free electrons. E electric current in gases is called a gas discharge. Thus, the current in gases is created by ions of both signs and electrons. A gas discharge with such a mechanism will be accompanied by the transfer of matter, i.e. ionized gases are conductors of the second kind.

In order to tear off one electron from a molecule or atom, it is necessary to perform a certain work A and, i.e. expend some energy. This energy is called ionization energy , whose values ​​for atoms various substances lie within 4–25 eV. Quantitatively, the ionization process is usually characterized by a quantity called ionization potential :

Simultaneously with the process of ionization in a gas, there is always a reverse process - the process of recombination: positive and negative ions or positive ions and electrons, meeting, recombine with each other to form neutral atoms and molecules. The more ions appear under the action of the ionizer, the more intense is the recombination process.

Strictly speaking, the electrical conductivity of a gas is never equal to zero, since it always contains free charges resulting from the action of radiation from radioactive substances present on the surface of the Earth, as well as from cosmic radiation. The intensity of ionization under the action of these factors is low. This slight electrical conductivity of the air is the cause of the leakage of charges of electrified bodies, even if they are well insulated.

The nature of the gas discharge is determined by the composition of the gas, its temperature and pressure, dimensions, configuration and material of the electrodes, as well as the applied voltage and current density.

Let us consider a circuit containing a gas gap (Fig.), subjected to continuous, constant in intensity action of an ionizer. As a result of the action of the ionizer, the gas acquires some electrical conductivity and current will flow in the circuit. Figure shows current-voltage characteristics (dependence of current on applied voltage) for two ionizers. Performance
(the number of pairs of ions produced by the ionizer in the gas gap in 1 second) of the second ionizer is greater than the first. We will assume that the performance of the ionizer is constant and equal to n 0 . At a not very low pressure, almost all the split off electrons are captured by neutral molecules, forming negatively charged ions. Taking recombination into account, we assume that the concentrations of ions of both signs are the same and equal to n. The average drift velocities of ions of different signs in an electric field are different: , . b - and b + are the mobility of gas ions. Now for region I, taking into account (5), we can write:

As can be seen, in region I, with increasing voltage, the current increases, since the drift velocity increases. The number of pairs of recombining ions will decrease as their speed increases.

Region II - saturation current region - all ions created by the ionizer reach the electrodes without having time to recombine. Saturation current density

j n = q n 0 d, (28)

where d is the width of the gas gap (the distance between the electrodes). As can be seen from (28), the saturation current is a measure of the ionizing effect of the ionizer.

At a voltage greater than U p p (region III), the speed of electrons reaches such a value that, when colliding with neutral molecules, they are able to cause impact ionization. As a result, additional An 0 pairs of ions are formed. The value A is called the gas amplification factor . In region III, this coefficient does not depend on n 0 , but depends on U. Thus. the charge reaching the electrodes at constant U is directly proportional to the performance of the ionizer - n 0 and voltage U. For this reason, region III is called the proportional region. U pr - proportionality threshold. The gas amplification factor A has values ​​from 1 to 10 4 .

In region IV, the region of partial proportionality, the gas gain begins to depend on n 0. This dependence increases with increasing U. The current increases sharply.

In the voltage range 0 ÷ U g, the current in the gas exists only when the ionizer is in operation. If the action of the ionizer is stopped, then the discharge also stops. Discharges that exist only under the action of external ionizers are called non-self-sustaining.

The voltage U g is the threshold of the region, the Geiger region, which corresponds to the state when the process in the gas gap does not disappear even after the ionizer is turned off, i.e. the discharge acquires the character of an independent discharge. Primary ions only give impetus to the occurrence of a gas discharge. In this region, I already acquire the ability to ionize massive ions of both signs. The magnitude of the current does not depend on n 0 .

In area VI, the voltage is so high that the discharge, once it has occurred, no longer stops - the area of ​​\u200b\u200bcontinuous discharge.

INDEPENDENT GAS DISCHARGE AND ITS TYPES

The discharge in the gas, which persists after the termination of the action of the external ionizer, is called independent.

Let us consider the conditions for the occurrence of an independent discharge. At high voltages (regions V–VI), the electrons that arise under the action of an external ionizer and are strongly accelerated by an electric field collide with neutral gas molecules and ionize them. As a result, secondary electrons and positive ions are formed. (process 1 in Fig. 158). Positive ions move towards the cathode and electrons move towards the anode. Secondary electrons again ionize the gas molecules, and, consequently, the total number of electrons and ions will increase as the electrons move towards the anode like an avalanche. This is the reason for the increase in electric current (see Fig. area V). The described process is called impact ionization.

However, impact ionization under the action of electrons is not enough to maintain the discharge when the external ionizer is removed. For this, it is necessary that the electron avalanches be "reproduced", i.e., that new electrons arise in the gas under the influence of some processes. Such processes are schematically shown in Fig. 158: Positive ions accelerated by the field, hitting the cathode, knock out electrons from it (process 2); Positive ions, colliding with gas molecules, transfer them to an excited state, the transition of such molecules to the normal state is accompanied by the emission of a photon (process 3); A photon absorbed by a neutral molecule ionizes it, the so-called process of photon ionization of molecules occurs (process 4); Knocking out electrons from the cathode under the action of photons (process 5).

Finally, at significant voltages between the electrodes of the gas gap, there comes a moment when positive ions, which have a shorter mean free path than electrons, acquire energy sufficient to ionize gas molecules (process 6), and ion avalanches rush to the negative plate. When, in addition to electron avalanches, ion avalanches also occur, the current increases almost without increasing the voltage (region VI in Fig.).

As a result of the described processes, the number of ions and electrons in the volume of the gas increases like an avalanche, and the discharge becomes independent, i.e., it persists even after the action of the external ionizer is terminated. The voltage at which self-discharge occurs is called the breakdown voltage. For air, this is about 30,000 volts for every centimeter of distance.

Depending on the gas pressure, the configuration of the electrodes, and the parameters of the external circuit, we can speak of four types of independent discharge: glow, spark, arc, and corona.

1. Smoldering discharge. Occurs at low pressures. If a constant voltage of several hundred volts is applied to the electrodes soldered into a glass tube 30 ÷ 50 cm long, gradually pumping air out of the tube, then at a pressure of ≈ 5.3 ÷ 6.7 kPa, a discharge occurs in the form of a glowing reddish winding cord, going from the cathode to the anode. With a further decrease in pressure, the cord thickens, and at a pressure of ≈ 13 Pa, the discharge has the form shown schematically in Fig.

Directly adjacent to the cathode is a thin luminous layer 1 - the first cathode glow, or a cathode film, then follows a dark layer 2 - a cathode dark space, passing further into a luminous layer 3 - a smoldering glow that has a sharp border on the cathode side, gradually disappearing from the anode side. It arises from the recombination of electrons with positive ions. The smoldering glow is bordered by a dark gap 4 - Faraday dark space, followed by a column of ionized luminous gas 5 - a positive column. The positive column has no significant role in maintaining the discharge. For example, as the distance between the electrodes of the tube decreases, its length shortens, while the cathode parts of the discharge remain unchanged in shape and size. In a glow discharge, only two of its parts are of particular importance for its maintenance: the cathode dark space and the glow glow. In the cathode dark space, a strong acceleration of electrons and positive ions occurs, knocking out electrons from the cathode (secondary emission). In the smoldering region, however, impact ionization of gas molecules by electrons occurs. The positive ions formed in this case rush to the cathode and knock out new electrons from it, which, in turn, again ionize the gas, etc. In this way, a glow discharge is continuously maintained.

With further evacuation of the tube at a pressure of ≈ 1.3 Pa, the glow of the gas weakens and the walls of the tube begin to glow. Electrons knocked out of the cathode by positive ions rarely collide with gas molecules at such rarefaction and therefore, accelerated by the field, hitting the glass, cause its glow, the so-called cathodoluminescence. The flow of these electrons has historically been called cathode rays.

Glow discharge is widely used in technology. Since the glow of the positive column has a color characteristic of each gas, it is used in gas-light tubes for luminous inscriptions and advertisements (for example, neon discharge tubes give a red glow, argon tubes - bluish-green). In fluorescent lamps, which are more economical than incandescent lamps, the glow discharge radiation occurring in mercury vapor is absorbed by a fluorescent substance (phosphor) deposited on the inner surface of the tube, which begins to glow under the influence of absorbed radiation. The luminescence spectrum with an appropriate selection of phosphors is close to the spectrum of solar radiation. Glow discharge is used for cathode deposition of metals. The cathode substance in a glow discharge due to bombardment by positive ions, being strongly heated, passes into a vapor state. By placing various objects near the cathode, they can be covered with a uniform layer of metal.

2. Spark discharge. Occurs at high electric field strengths (≈ 3·10 6 V/m) in a gas under atmospheric pressure. The spark has the appearance of a brightly luminous thin channel, curved and branched in a complicated way.

The explanation of the spark discharge is given on the basis of the streamer theory, according to which the appearance of a brightly luminous spark channel is preceded by the appearance of weakly luminous accumulations of ionized gas. These clusters are called streamers. Streamers arise not only as a result of the formation of electron avalanches through impact ionization, but also as a result of photon ionization of the gas. The avalanches, chasing each other, form conducting bridges of streamers, along which, at the next moments of time, powerful flows of electrons rush, forming spark discharge channels. Due to the release of a large amount of energy during the considered processes, the gas in the spark gap is heated to a very high temperature (about 10 4 K), which leads to its glow. The rapid heating of the gas leads to an increase in pressure and shock waves, which explain the sound effects of a spark discharge - the characteristic crackling in weak discharges and powerful thunder in the case of lightning, which is an example of a powerful spark discharge between a thundercloud and the Earth or between two thunderclouds.

The spark discharge is used to ignite the combustible mixture in internal combustion engines and to protect electrical transmission lines from surges (spark gaps). With a small length of the discharge gap, the spark discharge causes destruction (erosion) of the metal surface; therefore, it is used for electrospark precision machining of metals (cutting, drilling). It is used in spectral analysis to register charged particles (spark counters).

3. Arc discharge. If, after ignition of a spark discharge from a powerful source, the distance between the electrodes is gradually reduced, then the discharge becomes continuous - an arc discharge occurs. In this case, the current strength increases sharply, reaching hundreds of amperes, and the voltage across the discharge gap drops to several tens of volts. An arc discharge can be obtained from a low voltage source bypassing the spark stage. To do this, the electrodes (for example, carbon ones) are brought together until they touch, they are very hot with an electric current, then they are bred and obtained electric arc(this is how it was discovered by the Russian scientist V.V. Petrov). At atmospheric pressure, the temperature of the cathode is approximately equal to 3900 K. As the arc burns, the carbon cathode sharpens, and a depression forms on the anode - a crater, which is the hottest point of the arc.

According to modern concepts, the arc discharge is maintained due to the high temperature of the cathode due to intense thermionic emission, as well as thermal ionization of molecules due to the high temperature of the gas.

The arc discharge is widely used in national economy for welding and cutting metals, obtaining high-quality steels (arc furnace), lighting (spotlights, projection equipment). Arc lamps with mercury electrodes in quartz cylinders are also widely used, where an arc discharge occurs in mercury vapor when the air is pumped out. The arc generated in mercury vapor is a powerful source of ultraviolet radiation and is used in medicine (for example, quartz lamps). Arc discharge at low pressures in mercury vapor is used in mercury rectifiers to rectify alternating current.

4. corona discharge - high-voltage electrical discharge that occurs at high (for example, atmospheric) pressure in an inhomogeneous field (for example, near electrodes with a large curvature of the surface, the tip of a needle electrode). When the field strength near the tip reaches 30 kV/cm, a corona-like glow appears around it, which is the reason for the name of this type of discharge.

Depending on the sign of the corona electrode, a negative or positive corona is distinguished. In the case of a negative corona, the production of electrons that cause impact ionization of gas molecules occurs due to their emission from the cathode under the action of positive ions, in the case of a positive corona, due to gas ionization near the anode. AT vivo the corona occurs under the influence of atmospheric electricity at the tops of the masts of ships or trees (the action of lightning rods is based on this). This phenomenon was in ancient times called the fires of St. Elmo. The harmful effect of the corona around the wires of high-voltage power lines is the occurrence of leakage currents. To reduce them, the wires of high-voltage lines are made thick. The corona discharge, being discontinuous, also becomes a source of radio interference.

Corona discharge is used in electrostatic precipitators used for cleaning industrial gases from impurities. The gas to be purified moves from bottom to top in a vertical cylinder, along the axis of which a corona wire is located. The ions present in in large numbers in the outer part of the corona, impurities settle on the particles and are carried away by the field to the external non-corona electrode and settle on it. Corona discharge is also used in the application of powder and paint coatings.

ELECTROSTATIC FIELD

POWER LINES OF THE ELECTRIC FIELD

According to the concepts of modern physics, the effect of one charge on another is transmitted through electrostatic field - a special infinitely stretching material environment that each charged body creates around itself. Electrostatic fields cannot be detected by the human senses. However, a charge placed in a field is affected by a force directly proportional to the magnitude of this charge. Because the direction of the force depends on the sign of the charge, it was agreed to use the so-called trial charge q0. This is a positive, point charge, which is placed at the point of interest to us in the electric field. Accordingly, it is advisable to use the ratio of the force to the value of the test charge q 0 as a force characteristic of the field:

This constant for each point of the field is a vector quantity equal to strength acting on a unit positive charge is called tension . For the field of a point charge q at a distance r from it:

, (4)

The direction of the vector coincides with the direction of the force acting on the trial charge. [E] = N / C or V / m.

In a dielectric medium, the force of interaction between charges, and hence the field strength, decreases by ε times:

, . (5)

When several electrostatic fields are superimposed on each other, the resulting strength is determined as the vector sum of the strengths of each of the fields (superposition principle):

Graphically, the distribution of the electric field in space is depicted using lines of force . These lines are drawn so that the tangents to them at any point coincide with. This means that the vector of the force acting on the charge, and hence the vector of its acceleration, also lie on tangents to the lines of force, which never and nowhere intersect. The lines of force of an electrostatic field cannot be closed. They start on positive and end on negative charges or go to infinity.