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, electric field lines have a number of general properties(compare with the properties of fluid flow lines):
 1. Power lines do not intersect (otherwise, at the point of intersection, two tangents can be constructed, that is, at one point, the field strength has two values, which is absurd).
  2. Lines of force do not have breaks (at the break point, two tangents can again be constructed).
  3. Electrostatic field lines begin and end at charges.
  Since the field strength is determined at each spatial point, the field line 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 textbooks It is recommended to build a picture of the field lines so that their density is greater where the field strength is greater. This requirement is not strict, and not always feasible, so lines of force are drawn, satisfying the formulated properties 1 − 3 .
  It is very easy to construct the field lines of the field created by a point charge. In this case, the lines of force are a set of straight lines leaving (for positive) or entering (for negative) to the point where the charge is located (Fig. 234).

rice. 234
  Such families of field lines of point charge fields demonstrate that the charges are sources of the field, analogous to the sources and sinks of the fluid velocity field. We will prove later that lines of force cannot begin or end at those 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 it into it small portion semolina. If the oil and cereal are placed in an electrostatic field, then the grains of semolina (they have a slightly elongated shape) rotate in the direction of the electric field strength and line up approximately along the lines of force; after several tens of seconds, a picture of the electric field lines appears in the cup. Some of these “pictures” are presented in photographs.
  It is also possible to carry out theoretical calculations and construction of field lines. True, these calculations require an enormous number of calculations, so they are actually (and without much difficulty) 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 require resolution. 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 construct many segments of tangents to the lines of force, that is, segments of short 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 tension vector at a given point E x, E y and the modulus of this vector E = √(E x 2 + E y 2 ). Then you can construct a short segment, the direction of which coincides with the direction of the field strength vector. its projections on the coordinate axes are calculated using 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 field lines 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 absolute value, in fig. c), d) are different - we propose to determine which one is better on your own. Also determine the directions of the field lines in each case yourself.
  It is interesting to note that M. Faraday considered electric field lines as real elastic tubes connecting electric charges with each other; such ideas greatly helped him 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.

ELECTROSTATIC FIELD

electrostatic field test charge q 0

tension

, (4)

, . (5)

power lines

WORK OF ELECTROSTATIC FIELD FORCES. POTENTIAL

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

A 1,2 = 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 an energy characteristic of an electrostatic field, the ratio of the potential energy of a test charge q 0 placed at any point in the field to the value of this charge is used:

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

If we accept that when charge q 0 moves away to infinity (r→ ∞), its potential energy in the field of charge q becomes zero, then the potential of the field of a point charge q at a distance r from it:

. (9)

If a 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

SELF-SELF-SUSTAINED GAS DISCHARGE

Gases are good insulators at temperatures that are not too high and at pressures close to atmospheric. If you place a charged electrometer in dry atmospheric air, 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. To ionize, the gas must be exposed to some kind of ionizer: for example, an electric discharge, x-ray radiation, radiation or UV radiation, candle flame, etc. (V the latter case electrical conductivity of gas is caused by heating).

When gases are ionized, they escape from the external electron shell an atom or molecule with one or more electrons, resulting in the formation of free electrons and positive ions. Electrons can attach to neutral molecules and atoms, turning them into negative ions. Therefore, an ionized gas contains positively and negatively charged ions and free electrons. E Electric current in gases is called 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 classified as conductors of the second type.

In order to remove one electron from a molecule or atom, it is necessary to perform a certain amount of 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. The ionization process is usually characterized quantitatively by a quantity called ionization potential :

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

Strictly speaking, the electrical conductivity of a gas is never zero, since it always contains free charges formed as a result of the action of radiation from radioactive substances present on the surface of the Earth, as well as cosmic radiation. The intensity of ionization under the influence of these factors is low. This insignificant electrical conductivity of the air causes the leakage of charges from 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, the size, 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-intensity exposure to an ionizer. As a result of the action of the ionizer, the gas acquires some electrical conductivity and current flows in the circuit. Figure shows the current-voltage characteristics (current versus applied voltage) for two ionizers. Performance
(the number of ion pairs 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 productivity of the ionizer is constant and equal to n 0. At not very low pressure, almost all of the detached electrons are captured by neutral molecules, forming negatively charged ions. Taking into account recombination, 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 + – 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, as the drift speed increases. The number of pairs of recombining ions will decrease as their speed increases.

Region II - the region of saturation current - 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 they collide with neutral molecules they are capable of causing impact ionization. As a result, additional An 0 ion pairs are formed. The quantity A is called the gas gain coefficient . 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 the voltage U. For this reason, region III is called the proportionality 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, current in the gas exists only when the ionizer is active. If the action of the ionizer is stopped, the discharge also stops. Discharges that exist only under the influence of external ionizers are called non-self-sustaining.

Voltage Ug 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, massive ions of both signs also acquire the ability to ionize. The magnitude of the current does not depend on n 0 .

In region VI, the voltage is so high that the discharge, once occurring, does not stop - the region of continuous discharge.

SELF-INDEPENDENT GAS DISCHARGE AND ITS TYPES

A discharge in a gas that persists after the external ionizer stops working is called self-discharge.

Let us consider the conditions for the occurrence of a self-sustained discharge. At high voltages (regions V–VI), electrons generated under the action of an external ionizer, strongly accelerated by the 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 re-ionize the gas molecules, and, therefore, total quantity electrons and ions will increase as the electrons move towards the anode like an avalanche. This causes an increase in electric current (see Fig. Area V). The described process is called impact ionization.

However, impact ionization under the influence of electrons is not enough to maintain the discharge when the external ionizer is removed. To do this, it is necessary that electron avalanches be “reproduced,” that is, that new electrons arise in the gas under the influence of some processes. Such processes are shown schematically in Fig. 158: Positive ions accelerated by the field, hitting the cathode, knock electrons out of it (process 2); Positive ions, colliding with gas molecules, transfer them to an excited state, the transition of such molecules to a 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); Knockout of electrons from the cathode under the influence of photons (process 5).

Finally, at significant voltages between the electrodes of the gas gap, a moment comes when positive ions, which have a shorter 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 strength increases practically without an increase in voltage (region VI in the figure).

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

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

1. Glow discharge. Occurs at low pressures. If to the electrodes soldered into glass tube 30÷50 cm long, apply a constant voltage of several hundred volts, 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 luminous, winding reddish cord running 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 schematically shown in Fig.

Directly adjacent to the cathode is a thin luminous layer 1 - the first cathode glow, or cathode film, followed by a dark layer 2 - the cathode dark space, which then passes into the luminous layer 3 - a smoldering glow, which has a sharp boundary on the cathode side, gradually disappearing on the anode side. It occurs due to the recombination of electrons with positive ions. The smoldering glow is bordered by a dark gap 4 - the Faraday dark space, followed by a column of ionized luminous gas 5 - the positive column. The positive column does not have a significant role in maintaining the discharge. For example, when the distance between the electrodes of the tube decreases, its length decreases, while the cathode parts of the discharge remain unchanged in shape and size. In a glow discharge special meaning only two parts of it have to maintain it: the cathode dark space and the smoldering glow. In the cathode dark space, there is a strong acceleration of electrons and positive ions, knocking electrons out of the cathode (secondary emission). In the region of smoldering glow, 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, the glow discharge is continuously maintained.

With further pumping 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 at such rarefaction rarely collide with gas molecules and therefore, accelerated by the field, hitting the glass, causing it to glow, the so-called cathodoluminescence. The flow of these electrons was historically 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 gas-discharge tubes give a red glow, argon - 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 the absorbed radiation. The luminescence spectrum with appropriate selection of phosphors is close to the spectrum solar radiation. Glow discharge is used for cathode deposition of metals. The cathode substance in a glow discharge, due to bombardment with positive ions, becomes very hot and goes into a vapor state. By placing various objects near the cathode, they can be coated 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 glowing thin channel, complexly curved and branched.

The explanation of the spark discharge is given on the basis of the streamer theory, according to which the appearance of a brightly glowing spark channel is preceded by the appearance of faintly glowing 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. Avalanches, catching up with each other, form conducting bridges from 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 processes considered, the gas in the spark gap is heated to a very high temperature (approximately 10 4 K), which leads to its glow. Rapid heating of the gas leads to an increase in pressure and the formation of shock waves, which explain the sound effects of a spark discharge - the characteristic crackling sound in weak discharges and powerful thunderclaps in the case of lightning, which is an example of a powerful spark discharge between a thundercloud and the Earth or between two thunderclouds.

A spark discharge is used to ignite a combustible mixture in engines internal combustion and protection of electrical transmission lines from overvoltages (spark gaps). When the length of the discharge gap is short, the spark discharge causes destruction (erosion) of the metal surface, so it is used for electric spark precision processing of metals (cutting, drilling). It is used in spectral analysis to register charged particles (spark counters).

3. Arc discharge. If, after igniting 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 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, electrodes (for example, carbon) are brought together until they touch; they become very hot electric shock, then they are separated and an electric arc is obtained (this is how it was discovered by the Russian scientist V.V. Petrov). At atmospheric pressure, the temperature of the cathode is approximately 3900 K. As the arc burns, the carbon cathode becomes sharper, and a depression is formed on the anode - a crater, which is the hottest point of the arc.

By modern ideas, 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 caused by high temperature gas

Arc discharge is widely used in national economy for welding and cutting metals, producing high-quality steels (arc furnace), lighting (spotlights, projection equipment). Arc lamps with mercury electrodes in quartz cylinders are also widely used, where the arc discharge occurs in mercury vapor with evacuated air. The arc that occurs 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 – a high-voltage electrical discharge that occurs at high (for example, atmospheric) pressure in a non-uniform 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 glow appears around it, having the appearance of a crown, which is what gives rise to 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 birth of electrons that cause impact ionization of gas molecules occurs due to their emission from the cathode under the influence of positive ions, in the case of a positive corona, due to ionization of the gas near the anode. IN natural conditions the corona appears 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 called in ancient times the fires of St. Elmo. The harmful effect of 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. Corona discharge, being intermittent, also becomes a source of radio interference.

Corona discharge is used in electric precipitators used to purify 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. Ions present in large quantities in the outer part of the corona, they settle on impurity particles and are carried away by the field to the external non-corona electrode and settle on it. Corona discharge is also used when applying powder and paint coatings.

ELECTROSTATIC FIELD

ELECTRIC FIELD LINES

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

This constant vector quantity for each point of the field equal to the force 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 test 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 power lines . These lines are drawn so that the tangents to them at any point coincide with. This means that the vector of force acting on the charge, and therefore the vector of its acceleration, also lies on the tangents to the lines of force, which never intersect anywhere. Electrostatic field lines cannot be closed. They start on positive and end on negative charges or go to infinity.

Electric charge (amount of electricity) is a physical scalar quantity that determines the ability of bodies to be a source of electromagnetic fields and to take part in electromagnetic interaction. Electric charge was first introduced in Coulomb's law in 1785.

The unit of measurement of charge in the International System of Units (SI) is the coulomb - an electric charge passing through the cross section of a conductor at a current strength of 1 A for a time of 1 s. The charge of one pendant is very large. If two charge carriers ( q 1 = q 2 = 1 C) were placed in a vacuum at a distance of 1 m, then they would interact with a force of 9·10 9 N, that is, with the force with which the Earth’s gravity would attract an object with a mass of about 1 million tons. Electric charge closed system is preserved in time and is quantized - changes in portions that are multiples of the elementary electric charge, that is, in other words, an algebraic sum electric charges bodies or particles forming an electrically isolated system does not change during any processes occurring in this system.

Charge interaction The simplest and most everyday phenomenon in which the fact of the existence of electric charges in nature is revealed is the electrification of bodies upon contact. The ability of electric charges to both mutual attraction and mutual repulsion is explained by the existence of two various types charges One type of electric charge is called positive, and the other - negative. Oppositely charged bodies attract, and similarly charged bodies repel each other.

When two electrically neutral bodies come into contact as a result of friction, charges transfer from one body to another. In each of them, the equality of the sum of positive and negative charges is violated, and the bodies are charged differently.

When a body is electrified through influence, the uniform distribution of charges in it is disrupted. They are redistributed so that an excess of positive charges appears in one part of the body, and negative charges in another. If these two parts are separated, they will be charged oppositely.

Law of conservation of el. Charge In the system under consideration, new electrically charged particles can be formed, for example, electrons - due to the phenomenon of ionization of atoms or molecules, ions - due to the phenomenon of electrolytic dissociation, etc. However, if the system is electrically isolated, then the algebraic sum of the charges of all particles, including again appeared in such a system is always equal to zero.

The law of conservation of electric charge is one of the fundamental laws of physics. It was first experimentally confirmed in 1843 by the English scientist Michael Faraday and is currently considered one of the fundamental laws of conservation in physics (similar to the laws of conservation of momentum and energy). Increasingly sensitive experimental tests of the law of conservation of charge, which continue to this day, have not yet revealed deviations from this law.

. Electric charge and its discreteness. Law of conservation of charge. The law of conservation of electric charge states that the algebraic sum of the charges of an electrically closed system is conserved. q, Q, e – designations of electric charge. SI units of charge [q]=C (Coulomb). 1 mC = 10-3 C; 1 µC = 10-6 C; 1nC = 10-9 C; e = 1.6∙10-19 C – elementary charge. Elementary charge, e, is the minimum charge found in nature. Electron: qe = - e - electron charge; m = 9.1∙10-31 kg – mass of electron and positron. Positron, proton: qp = + e – charge of the positron and proton. Any charged body contains an integer number of elementary charges: q = ± Ne; (1) Formula (1) expresses the principle of discreteness of the electric charge, where N = 1,2,3... is a positive integer. Law of conservation of electric charge: the charge of an electrically isolated system does not change over time: q = const. Coulomb's law– one of the basic laws of electrostatics, which determines the force of interaction between two point electric charges.

The law was established in 1785 by Ch. Coulomb using the torsion balances he invented. Coulomb was interested not so much in electricity as in the manufacture of devices. Having invented an extremely sensitive device for measuring force - a torsion balance, he looked for possibilities for its use.

For suspension, the pendant used a silk thread 10 cm long, which rotated 1° with a force of 3 * 10 -9 gf. Using this device, he established that the force of interaction between two electric charges and between two poles of magnets is inversely proportional to the square of the distance between the charges or poles.

Two point charges interact with each other in a vacuum with a force F , the value of which is proportional to the product of charges e 1 And e 2 and inversely proportional to the square of the distance r between them:

Proportionality factor k depends on the choice of the system of measurement units (in the Gaussian system of units k= 1, in SI

ε 0 – electrical constant).

Strength F is directed along a straight line connecting charges, and corresponds to attraction for unlike charges and repulsion for like charges.

If interacting charges are in a homogeneous dielectric, with dielectric constant ε , then the interaction force decreases in ε once:

Coulomb's law is also the law that determines the force of interaction between two magnetic poles:

Where m 1 And m 2 – magnetic charges,

μ – magnetic permeability of the medium,

f – proportionality coefficient, depending on the choice of system of units.

Electric field– a separate form of manifestation (along with the magnetic field) of the electromagnetic field.

During the development of physics, there were two approaches to explaining the reasons for the interaction of electric charges.

According to the first version, force action between individual charged bodies was explained by the presence of intermediate links that transmit this action, i.e. the presence of a medium surrounding the body in which action is transmitted from point to point with a finite speed. This theory was called short range theory .

According to the second version, the action is transmitted instantly over any distance, while the intermediate medium may be completely absent. One charge instantly “feels” the presence of another, while no changes occur in the surrounding space. This theory was called long-range theory .

The concept of “electric field” was introduced by M. Faraday in the 30s of the 19th century.

According to Faraday, each charge at rest creates an electric field in the surrounding space. The field of one charge acts on another charge and on the other charge (the concept of short-range action).

An electric field created by stationary charges and not changing with time is called electrostatic. The electrostatic field characterizes the interaction of stationary charges.

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 point 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 the International System of Units (SI) is measured in volts per meter [V/m] or newtons per coulomb [N/C].

The force with which an electromagnetic field acts on charged particles[

The total force with which the electromagnetic field (generally including the electric and magnetic components) acts on a charged particle is expressed by the Lorentz force formula:

Where q- electric charge of the particle, - its speed, - vector of magnetic induction (main characteristic magnetic field), the oblique cross denotes the vector product. The formula is given in SI units.

Charges creating an electrostatic field can be distributed in space either discretely or continuously. In the first case, the field strength: n E = Σ Ei₃ i=t, where Ei is the strength at a certain point in space of the field created by one i-th charge system, and n is the total number of discrete charges that are part of the system. An example of solving a problem based on the principle of superposition of electric fields. So, to determine the strength of the electrostatic field, which is created in a vacuum by stationary point charges q₁, q₂, …, qn, we use the formula: n E = (1/4πε₀) Σ (qi/r³i)ri i=t, where ri is the radius vector , drawn from a point charge qi to the field point under consideration. Let's give another example. Determination of the strength of the electrostatic field, which is created in a vacuum by an electric dipole. An electric dipole is a system of two charges q>0 and –q, identical in absolute value and, at the same time, opposite in sign, the distance I between which is relatively small compared to the distance of the points under consideration. The dipole arm will be called the vector l, which is directed along the dipole axis towards the positive charge from the negative charge and is numerically equal to the distance I between them. Vector pₑ = ql is the electric moment of the dipole.

Strength E of the dipole field at any point: E = E₊ + E₋, where E₊ and E₋ are the field strengths of electric charges q and –q. Thus, at point A, which is located on the dipole axis, the dipole field strength in vacuum will be equal to E = (1/4πε₀)(2pₑ/r³) At point B, which is located on the perpendicular restored to the dipole axis from its middle: E = (1/4πε₀)(pₑ/r³) At an arbitrary point M, sufficiently distant from the dipole (r≥l), the modulus of its field strength is equal to E = (1/4πε₀)(pₑ/r³)√3cosϑ + 1 In addition the principle of superposition of electric fields consists of two statements: The Coulomb force of interaction between two charges does not depend on the presence of other charged bodies. Let us assume that charge q interacts with the system of charges q1, q2, . . . , qn. If each of the charges of the system acts on charge q with a force F₁, F₂, …, Fn, respectively, then the resulting force F applied to charge q by this system is equal to the vector sum of the individual forces: F = F₁ + F₂ + … + Fn. Thus, the principle of superposition of electric fields allows one to arrive at one important statement.

Electric field lines

The electric field is represented using lines of force.

Field lines indicate the direction of the force acting on a positive charge at a given point in the field.

Properties of electric field lines

Electric field lines have a beginning and an end. They start on positive charges and end on negative ones.

Electric field lines are always perpendicular to the surface of the conductor.

The distribution of electric field lines determines the nature of the field. The field may be radial(if the lines of force come out from one point or converge at one point), homogeneous(if the field lines are parallel) and heterogeneous(if the field lines are not parallel).

Charge density- this is the amount of charge per unit length, area or volume, thus determining the linear, surface and volumetric charge densities, which are measured in the SI system: in Coulombs per meter (C/m), in Coulombs per square meter(C/m²) and in Coulombs per cubic meter(C/m³), respectively. Unlike the density of matter, charge density can have both positive and negative values, this is due to the fact that there are positive and negative charges.

Linear, surface and volume charge densities are usually denoted by the functions , and, accordingly, where is the radius vector. Knowing these functions we can determine the total charge:

§5 Tension vector flow

Let us define the vector flow through an arbitrary surface dS, - the normal to the surface. α - the angle between the normal and the force line of the vector. You can enter an area vector. VECTOR FLOW called a scalar quantity F E equal to the scalar product of the intensity vector and the area vector

For a uniform field

For a non-uniform field

where is the projection, - is the projection.

In the case of a curved surface S, it must be divided into elementary surfaces dS, calculate the flux through an elementary surface, and the total flux will be equal to the sum or, in the limit, the integral of the elementary fluxes

where is the integral over a closed surface S (for example, over a sphere, cylinder, cube, etc.)

The vector flux is an algebraic quantity: it depends not only on the field configuration, but also on the choice of direction. For closed surfaces, the outer normal is taken as the positive direction of the normal, i.e. the normal pointing outward to the area covered by the surface.

For a uniform field, the flux through a closed surface is zero. In the case of a non-uniform field

3. The intensity of the electrostatic field created by a uniformly charged spherical surface.

Let a spherical surface of radius R (Fig. 13.7) carry a uniformly distributed charge q, i.e. the surface charge density at any point on the sphere will be the same.

Let us enclose our spherical surface in a symmetrical surface S with radius r>R. The flux of the tension vector through the surface S will be equal to

By Gauss's theorem

Hence

Comparing this relationship with the formula for the field strength of a point charge, we can come to the conclusion that the field strength outside the charged sphere is the same as if the entire charge of the sphere was concentrated at its center.

2. Electrostatic field of the ball.

Let us have a ball of radius R, uniformly charged with volume density.

At any point A lying outside the ball at a distance r from its center (r>R), its field is similar to the field of a point charge located in the center of the ball. Then out of the ball

and on its surface (r=R)

· Electric field lines have a beginning and an end. They start on positive charges and end on negative ones.

· Electric field lines are always perpendicular to the surface of the conductor.

· The distribution of electric field lines determines the nature of the field. The field may be radial(if the lines of force come out from one point or converge at one point), homogeneous(if the field lines are parallel) and heterogeneous(if the field lines are not parallel).

20) Let me remind you that these are the energy characteristics of the electric field.

The electric field potential at any point is defined as

.

and is equal to the potential energy of a unit charge introduced into a given point in the field.

If a charge is moved in a field from point 1 to point 2, then a potential difference arises between these points

.

The meaning of potential difference: this is the work of an electric field to move a charge from one point to another.

The field potential can also be interpreted through work. If point 2 is at infinity, where there is no field (), then - this is the work of the field to move a charge from a given point to infinity. The field potential created by a single charge is calculated as .

Surfaces at each point of which the field potentials are the same are called equipotential surfaces. In a dipole field, the potential surfaces are distributed as follows:

The field potential formed by several charges is calculated using the principle of superposition: .

a) Calculation of the potential at point A, located not on the dipole axis:

Let us find from the triangle ( ). Obviously, . That's why And .

.

b) Between points A and B, equidistant from the dipole at a distance

() the potential difference is defined as (we accept without the proof, which you will find in Remizov’s textbook)

.

c) It can be shown that if the dipole is located in the center of an equilateral triangle, then the potential difference between the vertices of the triangle are related as projections of the vector onto the sides of this triangle ( ).

21) - the work of the electric field along the power lines is calculated.

1. Work in an electric field does not depend on the shape of the path.

2. Work perpendicular to the lines of force is not performed.

3. In a closed loop, no work is done in an electric field.

Energy characteristics of the electric field (potanceal).

1) Physical meaning:

If Cl, then (numerically), provided that the charge placed at a given point in the electric field.

Unit:

2) Physical meaning:

If a unit positive point charge is placed at a given point, then (numerically), when moving from a given point to infinity.

Δφ is the difference between the dance values ​​of two points of the electric field.

U – voltage – “y” is the difference between the voltages of two points of the electric field.

[U]=V (Volt)

Physical meaning:

If , then (numerically) when moving from one point of the field to another.

Relationship between tension and tension:

22) In an electrostatic field, all points of a conductor have the same potential, which is proportional to the charge of the conductor, i.e. the ratio of charge q to potential φ does not depend on charge q. (Electrostatic is the field surrounding stationary charges). Therefore, it turned out to be possible to introduce the concept of electrical capacitance C of a solitary conductor:

Electrical capacity is a quantity numerically equal to the charge that must be imparted to the conductor in order for its potential to change by one.

Capacitance is determined by the geometric dimensions of the conductor, its shape and properties environment and does not depend on the conductor material.

Units of measurement for quantities included in the definition of capacity:

Capacitance - designation C, unit of measurement - Farad (Ф, F);

Electric charge - designation q, unit of measurement - coulomb (C, C);

φ - field potential - volts (V, V).

It is possible to create a system of conductors that will have a capacity much greater than an individual conductor, independent of the surrounding bodies. Such a system is called a capacitor. The simplest capacitor consists of two conducting plates located at a short distance from each other (Fig. 1.9). The electric field of a capacitor is concentrated between the plates of the capacitor, that is, inside it. Capacitor capacity:

C = q / (φ1 - φ2) = q / U

(φ1 - φ2) - potential difference between the plates of the capacitor, i.e. voltage.

The capacitance of a capacitor depends on its size, shape and dielectric constant ε of the dielectric located between the plates.

C = ε∙εo∙S / d, where

S - lining area;

d - distance between plates;

ε - permittivity dielectric between plates;

εo - electrical constant 8.85∙10-12F/m.

If it is necessary to increase the capacitance, the capacitors are connected to each other in parallel.

Fig.1.10. Parallel connection of capacitors.

Ctotal = C1 + C2 + C3

In a parallel connection, all capacitors are under the same voltage, and their total charge is Q. In this case, each capacitor will receive a charge Q1, Q2, Q3, ...

Q = Q1 + Q2 + Q3

Q1 = C1∙U; Q2 = C2∙U; Q3 = C3∙U. Let's substitute into the above equation:

C∙U = C1∙U + C2∙U + C3∙U, whence C = C1 + C2 + C3 (and so on for any number of capacitors).

For serial connection:

Fig.1.11. Series connection of capacitors.

1/Ctot = 1/C1 + 1/C2 + ∙∙∙∙∙ + 1/ Cn

Derivation of the formula:

Voltage on individual capacitors U1, U2, U3,..., Un. Total voltage of all capacitors:

U = U1 + U2 + ∙∙∙∙∙ + Un,

taking into account that U1 = Q/ C1; U2 = Q/ C2; Un = Q/ Cn, substituting and dividing by Q, we obtain a relationship for calculating the capacitance of a circuit with a series connection of capacitors

Capacitance units:

F - farad. This is a very large value, so smaller values ​​are used:

1 µF = 1 µF = 10-6F (microfarad);

1 nF = 1 nF = 10-9 F (nanofarad);

1 pF = 1pF = 10-12F (picofarad).

23) If a conductor is placed in an electric field then the force q will act on the free charges q in the conductor. As a result, a short-term movement of free charges occurs in the conductor. This process will end when the own electric field of the charges arising on the surface of the conductor completely compensates for the external field. The resulting electrostatic field inside the conductor will be zero (see § 43). However, in conductors, under certain conditions, continuous ordered movement of free electric charge carriers can occur. This movement is called electric current. The direction of the electric current is taken to be the direction of movement of positive free charges. For the existence of electric current in a conductor, two conditions must be met:

1) the presence of free charges in the conductor - current carriers;

2) the presence of an electric field in the conductor.

The quantitative measure of electric current is current strength I– scalar physical quantity equal to the ratio of the charge Δq transferred through the cross section of the conductor (Fig. 11.1) during the time interval Δt to this time interval:

The ordered movement of free current carriers in a conductor is characterized by the speed of the ordered movement of the carriers. This speed is called drift speed current carriers. Let a cylindrical conductor (Fig. 11.1) have a cross section with an area S. In the volume of the conductor, limited by cross sections 1 and 2 with a distance ∆ X between them contains the number of current carriers ∆ N= nS∆X, Where n– concentration of current carriers. Their total charge ∆q = q 0 ∆ N= q 0 nS∆X. If, under the influence of an electric field, current carriers move from left to right with a drift speed v dr, then in time ∆ t=∆x/v dr all carriers contained in this volume will pass through cross section 2 and create an electric current. The current strength is:

. (11.2)

Current density is the amount of electric current flowing through a unit cross-sectional area of ​​a conductor:

. (11.3)

In a metal conductor, the current carriers are free electrons of the metal. Let's find the drift speed of free electrons. With current I = 1A, cross-sectional area of ​​the conductor S= 1mm 2, concentration of free electrons (for example, in copper) n= 8.5·10 28 m --3 and q 0 = e = 1.6·10 –19 C we obtain:

v dr = .

We see that the speed of directional movement of electrons is very low, much less than the speed of chaotic thermal movement of free electrons.

If the strength of the current and its direction do not change over time, then such a current is called constant.

In the International System of Units (SI) current is measured in amperes (A). The current unit of 1 A is determined by the magnetic interaction of two parallel conductors with current.

A direct electric current can be created in a closed circuit in which free charge carriers circulate along closed trajectories. But when an electric charge moves in an electrostatic field along a closed path, the work done by electric forces is zero. Therefore, for the existence of direct current, it is necessary to have a device in the electrical circuit that is capable of creating and maintaining potential differences in sections of the circuit due to the work of forces of non-electrostatic origin. Such devices are called direct current sources. Forces of non-electrostatic origin acting on free charge carriers from current sources are called external forces.

The nature of external forces may vary. In galvanic cells or batteries they arise as a result of electrochemical processes; in direct current generators, external forces arise when conductors move in a magnetic field. Under the influence of external forces, electric charges move inside the current source against the forces of the electrostatic field, due to which a constant electric current can be maintained in a closed circuit.

When electric charges move along a direct current circuit, external forces acting inside the current sources perform work.

Physical quantity equal to the work ratio A st external forces when a charge q moves from the negative pole of a current source to the positive pole to the value of this charge is called the electromotive force of the source (EMF):

ε . (11.2)

Thus, the EMF is determined by the work done by external forces when moving a single positive charge. Electromotive force, like potential difference, is measured in volts (V).

When a single positive charge moves along a closed direct current circuit, the work done by external forces is equal to the sum of the emf acting in this circuit, and the work done by the electrostatic field is zero.

In the space surrounding the charge that is the source, the amount of this charge is directly proportional to the square and the distance from this charge is inversely proportional to the square. The direction of the electric field, according to accepted rules, is always from the positive charge towards the negative charge. This can be imagined as if you place a test charge in a region of space 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 intensity, which, being a vector quantity, can be represented graphically as an arrow with a length and direction. At any location, 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 further the region of space is from the source of the field (charge Q), the shorter the length of the tension vector. Moreover, the length of the vector decreases as it moves away n times from some place in n 2 times, that is, inversely proportional to the square.

More useful tool A visual representation of the vector nature of the electric field is the use of such a concept as, or simply lines of force. Instead of drawing countless vector arrows in space surrounding the source charge, it has proven useful to combine them into lines, where the vectors themselves are tangent to points on such lines.

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

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

Rules for drawing electric field lines

There are many rules for drawing up such models of electrical power lines. All these rules were created in order to provide the greatest information content when visualizing (drawing) the electric field. One way is to depict field lines. One of the most common ways is to surround more charged objects a large number lines, that is, a higher line density. Objects with more 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 the lines of force, and the greater the magnitude of the charge, the denser the lines around it.

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

It's important to remember that electric field lines do not intersect, and lines of another type - equipotential, form closed contours. At the point where two types of lines intersect, the tangents to these lines are mutually perpendicular. Thus, something like a curved coordinate grid, or 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 leaving charges and going to infinity. What will be the configuration of the field lines for two or more charges? To perform such a pattern, it is necessary to remember that we are dealing with a vector field, that is, with electric field strength vectors. To depict the field pattern, we need to add the voltage vectors from two or more charges. The resulting vectors will represent the total field of several charges. How can field lines be constructed in this case? It is important to remember that each point on a field line is single point contact with the electric field strength vector. This follows from the definition of a tangent in geometry. If we construct a perpendicular in the form of long lines from the beginning of each vector, then mutual intersection many such lines will depict the very sought-after line of force.

For a more accurate mathematical algebraic representation of the lines of force, it is necessary to draw up equations of the lines of force, and the vectors in this case will represent the first derivatives, lines of the first order, which are 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 strength vectors from each charge source. This warp 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 a slight one, 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 interaction that occurs between charged objects. The concept of an electric field was first introduced by 19th-century physicist Michael Faraday. This was the result of Michael Faraday's perception invisible reality in the form of a picture of field lines characterizing long-range action. Faraday did not think within the framework of one charge, but went further and expanded the boundaries of his mind. He proposed that a charged object (or mass in the case of gravity) influences space and introduced the concept of a field of such influence. By examining such fields, he was able to explain the behavior of charges and thereby revealed many of the secrets of electricity.