Breakdown in air and along the surface at high frequency - solid insulation of internal high-voltage structures. Breakdown at high voltage

Basic concepts about breakout

We looked at various physical phenomena, occurring in a dielectric under the influence of an electric field of not too high intensity, when the dielectric remains a practically non-conducting medium. However, electric field forces with a corresponding increase in tension can lead to a violation of this state. As a result, the dielectric will go from a non-conducting state to a state high conductivity, but not the entire sample to which voltage is applied, but only a narrow channel directed from one electrode to another.

The phenomenon of formation of a conducting channel in a dielectric under the influence of an electric field is called breakdown . There may be a breakdown complete , if a conducting channel passes from one electrode to another and closes them, incomplete , if the conductive channel does not reach at least one of the electrodes, and partial , if only a gas or liquid inclusion of a solid dielectric breaks through. In solid dielectrics, in addition to breakdown by volume, breakdown on the surface (in gas or liquid) is possible, called surface breakdown .

The minimum voltage applied to a dielectric sample leading to its breakdown is called breakdown voltage ().

Current-voltage characteristic of a dielectric sample (or electrical insulation), linear at ordinary voltages ( U), deviates from linear as it approaches U To U np(Fig. 9.13). At the moment of breakdown, the current through the dielectric increases sharply, so that . A spark or electric arc occurs at the site of the breakdown. Due to the formation of a plasma highly conductive breakdown channel between the electrodes, the sample becomes short-circuited, and the voltage across it drops, despite the increase in current.

Rice. 9.13. Current-voltage characteristics of electrical insulation

If a breakdown occurs in a gaseous or liquid dielectric, then due to the mobility of molecules, the broken area, after removing the voltage, restores its original properties and value UPp(but provided that the power and duration electric arc were not so significant as to cause significant changes in the dielectric throughout its entire volume). After a breakdown of a solid dielectric, a trace remains in it in the form of a punched (hence the name “breakdown”), burnt or melted hole, most often irregular shape. If the voltage is applied again, the breakdown, as a rule, occurs at the previously pierced place at a significantly reduced voltage.

In some cases, after a dielectric breakdown, conductive decomposition products remain in the breakdown channel, and the dielectric loses its electrical insulating properties. Damage to the surface of a solid dielectric associated with the formation of conductive traces (“tracks”) is called surface breakdown. tracking .

The rated voltage of the electrical insulation must be less than the breakdown voltage. size, equal to the ratio breakdown voltage to rated voltage is called electric strength safety factor .

Meaning U np dielectric is directly related to the time of voltage application. Thus, with short-term pulses, breakdown occurs at higher voltages than in the case of a constant or long-term applied alternating voltage.

Prolonged exposure to a high-intensity electric field leads to irreversible processes in the dielectric, as a result of which its breakdown voltage decreases, i.e. is happening electrical aging of insulation . Due to this aging, the insulation has a limited service life. Dependency curve U np from the time of application of voltage is called electrical insulation life curve . Breakdown voltage ( U np) increases with increasing dielectric thickness h.

To characterize the ability of a material to resist destruction in an electric field, the concept of electric field strength at which breakdown occurs is introduced:

The intensity of a uniform electric field leading to breakdown is called electrical strength . Electric strength ( E pr) is one of the most important parameters electrical insulating material.

The breakdown mechanisms of gaseous, liquid and solid dielectrics have significant differences.

Gas breakdown

The number of electrons formed within 1 s in 1 cm 3 of air under the influence of radioactivity of the Earth or cosmic rays, ranges from 10 to 20. These electrons are the initial charges leading to breakdown of the gas in a strong field. As the electric field strength increases, the electrons between two collisions acquire energy sufficient to ionize gas molecules.

At given values gas pressure and temperature, impact ionization begins at a certain field strength. This field strength ( E) is called initial tension .

In some gases (for example, oxygen, carbon dioxide, water vapor), the separated electron, during one of the next encounters with another neutral molecule, combines with it, turning it into an electronegative ion.

The main ionization is carried out by electrons. As a result, when they collide with atoms and molecules, they generate new electrons. The “secondary” electrons released under the influence of the field, in turn, cause the ionization of gas molecules. As a result of this process, the number of electrons in the gas gap, increasing like an avalanche, increases very quickly. Impact ionization by electrons forms the basis of gas breakdown.

A feature of gas breakdown in a non-uniform field is the occurrence of a partial discharge in the form crowns in places where the field strength reaches critical values, with further transition crowns in spark discharge and arc as the voltage increases.

Air breakdown at the surface of a solid dielectric, called surface flashing in technology, usually occurs at lower voltages than in the case when there is only air between the electrodes. The value of the discharge voltage is influenced by the shape of the electric field, determined by the configuration of the electrodes and dielectric, voltage frequency, state of the dielectric surface, and air pressure.

Breakdown of liquid dielectrics

Liquid dielectrics have significantly higher breakdown voltages than gases in normal conditions. The breakdown mechanism and the electrical strength of dielectric liquids depend primarily on their purity. Electrical breakdown thoroughly purified liquids under short-term exposure to an electric field occurs due to a combination of two processes: impact ionization by electrons and cold emission from the cathode. In accordance with this, the electrical strength of thoroughly purified liquids is two orders of magnitude higher than gases, and is approximately 100 MV/m. This is explained by the fact that a higher field strength is required in order for an electron to move in a denser medium with a shorter mean free path ( λ ), has accumulated energy sufficient for ionization.

The nature of the breakdown of contaminated and technically pure liquids is determined by processes associated with the movement and redistribution of impurity particles.

A sharp decline E pr It also occurs when the liquid is contaminated with wet organic fibers (paper, textiles), since such fibers are capable of forming bridges with increased conductivity. If the bridge comes into contact with one of the electrodes, then it serves as a needle-shaped continuation of this electrode, as a result of which the interelectrode distance decreases and the field inhomogeneity increases. In the case of “dry” fibers, the bridges have high resistance and have less influence on E pr liquids. The most common impurity in liquid dielectrics is moisture, which can be in a dissolved or emulsified state.

Breakdown of solid dielectrics

Physical picture of the breakdown of solid dielectrics in different cases may be different. Along with ionization processes, secondary processes caused by a strong electric field (heating, chemical reactions, partial discharges, mechanical stresses as a result of electrostriction, the formation of space charges at the boundaries of inhomogeneities, etc.). Therefore, several mechanisms of breakdown of solid dielectrics are distinguished: electrical, electrothermal, electrochemical and ionization.

Electrical breakdown is a breakdown caused by impact ionization or breaking of bonds between dielectric particles directly under the influence of an electric field.

Electric strength ( E pr) of solid dielectrics during electrical breakdown lies within relatively narrow limits – 100 – 1000 MV/m, which is close to E pr strongly compressed gases and very clean liquids. Meaning E pr mainly due to internal structure dielectric (packing density of atoms, strength of their bonds) and weakly depends on such external factors, such as temperature, frequency of applied voltage, shape and dimensions of the sample (except for very small thicknesses). This type of breakdown is typical for macroscopically homogeneous dielectrics with low dielectric losses. A breakdown of this type occurs in no more than 10 -7 ... 10 -8 s and is not caused by thermal energy. The value of electrical strength during electrical breakdown depends to some extent on temperature and is accompanied in its initial stage by the destruction of the dielectric in a very narrow channel.

Electrothermal (thermal ) breakdown is a breakdown caused by thermal processes occurring in a dielectric when exposed to an electric field and leading to the destruction of the dielectric. Thermal breakdown occurs when the amount of heat released in the dielectric due to dielectric losses, exceeds the amount of heat that can be dissipated under given conditions; in this case it is violated thermal equilibrium, and the process takes on an avalanche-like character.

The phenomenon of thermal breakdown comes down to heating the material in an electric field to temperatures corresponding to melting, cracking, charring, etc. The value of breakdown voltage during thermal breakdown is a characteristic of not only the material, but also the product, as opposed to electric and ionization breakdown, where breakdown voltage can serve characteristics of the material, namely its electrical strength.

The breakdown voltage caused by heating the dielectric depends on the voltage frequency, cooling conditions, temperature environment etc. In addition, the electrothermal (breakdown) voltage depends on the heat resistance of the material. Organic dielectrics (for example, polystyrene) have lower values ​​of “electrothermal” breakdown voltages than inorganic dielectrics (quartz, ceramics), with other equal conditions, if only due to their low heat resistance.

Electrochemical breakdown due to chemical processes, leading to changes in the dielectric under the influence of an electric field. Chemical changes(aging) at high voltage occur due to electrolysis, the presence of ozone in the air, etc. Electrical aging is especially significant when exposed to direct voltage and is less noticeable when exposed to alternating voltage.

Ionization breakdown – this is a breakdown caused by ionization processes due to partial discharges in the dielectric. It is most typical for dielectrics with air inclusions (for example, paper insulation). At high field strengths in the air pores, air ionization occurs, ozone formation, accelerated ions, heat generation. All these processes lead to the gradual destruction of insulation and a decrease in E pr.

As indicated, in solid dielectrics, in addition to volumetric, it is also possible surface breakdown , i.e. breakdown in a liquid or gaseous dielectric adjacent to the surface of solid insulation. Because E pr liquids and especially gases below E pr solid dielectrics, and the normal component of the electric field strength is continuous at the interface, then with the same distance between the electrodes in the bulk and on the surface, the breakdown will primarily occur along the surface of the solid dielectric. To prevent surface breakdown, it is necessary to extend possible way discharge on the surface. Therefore, the surface of the insulators is made corrugated, and non-metalized edges of the dielectric are left in the capacitors. Superficial Uetc They are also increased by sealing the surface of electrical insulation with varnishes, compounds, and liquid dielectrics with high electrical strength.

Breakdown of macroscopically inhomogeneous dielectrics

Most dielectrics used in practice have inhomogeneities various types. For example, ceramic dielectrics consist of several phases (crystalline and glassy), with different electrical properties, and have a greater or lesser number of pores (air inclusions). Pressed and wound products have a layered structure; their alternating layers also have unequal dielectric properties.

Due to small E pr, ε And γ gas inclusions of a porous dielectric located in a strong electric field, partial discharges arise (“ignite”) in these inclusions. It is the occurrence of these discharges that is often the main process leading to the breakdown of a porous dielectric (ionization breakdown).

To increase the electrical strength of porous dielectrics, they are impregnated, filling the pores with liquid or hardening electrical insulating material with high electrical strength. So, for unimpregnated cable paper E pr= 3...5MV/m, and for impregnated with compound E pr= 40...80 MV/m.

Now we will take a qualitative look at some of the characteristics of the fields around conductors. Let's charge a conductor with electricity, but this time not a spherical one, but one that has a tip or edge (for example, in the shape shown in Fig. 6.14). Then the field in this place will be much stronger than in other places. The reason is general outline consists in the fact that charges tend to spread as widely as possible over the surface of the conductor, and the tip of the tip is always farthest from the rest of the surface. Therefore, part of the charges on the plate flows towards the tip. Relatively small quantity charge on it can create a large surface density, A high density means a strong field near the conductor in this place.

In general, in those places of the conductor in which the radius of curvature is smaller, the field is stronger. To see this, consider a combination of a large and a small sphere connected by a wire, as shown in Fig. 6.15. The wire itself will not have much effect external margins; his job is to equalize the potentials of the spheres. Near which ball will the field be more intense? If the radius of the left ball A, and the charge Q,

(Of course, the presence of one ball will affect the distribution of charges on the other, so that in fact none of them will have charges distributed symmetrically. But if we are only interested in the approximate magnitude of the field, then we can use the formula for the potential of a spherical charge.) If less ball radius b has a charge q, then its potential is approximately equal

But φ 1 =φ 2 so

On the other hand, the field near the surface [see equation (5.8)] is proportional surface density charge, which in turn is proportional to the total charge divided by the square of the radius. It turns out that

This means that the surface of the smaller sphere has a larger field. The fields are inversely proportional to the radii.

This result is very important from a technical point of view, because a breakdown occurs in the air if the field is too large. Some free charge in the air (an electron or ion) is accelerated by this field, and if it is very strong, then the charge can gain such a speed before colliding with an atom that it will knock out a new electron from the atom. As a result, more and more ions appear. Their movement constitutes a spark, or discharge. If you want to charge a body to a high potential without it being discharged into the air, you must be sure that the surface of the body is smooth and that there are no places where the field is too high.

In gases, only electrical breakdown is observed.

In gaseous dielectrics there is a certain amount of free ions and electrons, which, under the influence of an electric field, begin to move towards the anode. Important role during breakdown, especially in the initial stage, belongs to electrons as particles that have much greater mobility than ions. When an electron collides with a molecule, it transfers part of its energy to it, after which two scenarios are possible, which can be described in a simplified manner as follows:

1. the molecule is ionized, emitting an electron, thus two electrons move (accelerating in the field), which can ionize two other molecules and now four are moving free electron, which can ionize the next four molecules - as a result, impact ionization is observed leading to the occurrence of an electron avalanche;

2. the molecule goes into an excited state and gives off excess energy in the form of radiation - a photon, which can ionize another molecule, thus photon ionization occurs, leading to the appearance of a channel with increased conductivity (streamer).

Photons moving at the speed of light (3 10 8 m/s), are ahead of electron avalanches and, when they “collide” with neutral molecules, ionize them, giving rise to new electron (“daughter”) avalanches.

The main and daughter avalanches, moving towards the anode, grow, catch up with each other, merge and form an electronegative streamer - a chain of electron avalanches merging into a single whole. A stream of positive ions is also formed, which moves in the opposite direction, forming an electropositive streamer. Approaching the cathode, positive ions, hitting its surface, form a luminous cathode spot emitting “secondary” electrons. The positive streamer, being filled with secondary electrons and electrons formed as a result of electron impact ionization and photoionization, turns into a through channel of gas-discharge plasma. The electrical conductivity of this channel is very high, and a short circuit current flows through it Ishort circuit.

Figure 5.9 shows a diagram explaining the development of electrical breakdown, where avalanches are conventionally shown in the form of shaded cones, and the paths of photons are depicted by wavy lines. The origins of the wavy lines come from atoms that have been excited by an electron and then emitted a photon.

Rice. 5.9. Schematic representation of an electron avalanche and the formation of an electronegative streamer during gas breakdown

The formation of a plasma gas-discharge channel (Figure 5.10) is actually a breakdown of gases. Emergence Ishort circuit- a consequence of a breakdown. Depending on the size Ishort circuit breakdown manifests itself in the form of a spark or electric arc.

Rice. 5.10. Schematic representation of the formation of a gas-discharge plasma channel

Gas breakdown in a constant uniform field is characterized by the dependence E depending on pressure (Figure 5.11.a). At pressure values ​​above normal, the gas is compressed and, consequently, the mean free path of the electron decreases. Therefore, to satisfy the condition for the possibility of breakdown, it is necessary to increase the electric field strength E. When the gas is low average length the free path of the electron increases, and at the same time the electrons can acquire additional energy even at a lower value of the field strength. In area high vacuum E pr increases because, as a result of strong rarefaction of the gas, the number of molecules per unit volume decreases and the probability of collisions of electrons with molecules decreases. A pressure of 0.1 MPa corresponds to normal atmospheric pressure.

E air in a uniform field increases, as shown in Figure 5.11 b), with a decrease in the distance between the electrodes due to a decrease in the probability of collisions of electrons with gas molecules. Increase in electrical strength in in this case caused by the difficulty of forming a discharge due to the small distance between the electrodes.

The breakdown voltage of gases is significantly reduced in inhomogeneous fields, for example, for air at d=1 cm from 30 kV to 9 kV.

Rice. 5.11. Dependence of electrical strength of gas on pressure

Paschen's law. Paschen's law shows the dependence U np gaseous dielectrics in a specific design from the product of pressure R gas to a distance h between the electrodes (Fig. 5.12). The law establishes that each gas has its own minimum breakdown voltage value U np.min depending on the work Ph. For gases consisting of di- and polyatomic molecules, Upr.min lies in the range from 280 V (H 2) to 420 V (CO 2). At a frequency of 50 Hz in non-ionized air in a uniform electric field Upr.min~ 326 V. For inert gases (gases consisting of monatomic molecules) Upr.min, lower than that of gases made of polyatomic molecules (for example, pure argon Upr.min≈195 V, and for argon with an admixture of sodium vapor ~ 95 V, for neon with sodium vapor ~ 85 V). Therefore, to reduce Upr.min inert gases used in gas-discharge devices, the electrodes are made (or at least coated) from metals with additives of alkali or alkaline earth metals having little work electron release.

In a non-uniform field on U The polarity of the electrodes also influences. Thus, for electrodes with a small radius of curvature U pr with positive polarity are lower than with negative polarity. This is due to the formation of a positive space charge at the tip as a result of the development of a corona discharge, which leads to an increase in the field strength in the rest of the gap.

Rice. 5.12. Dependence of breakdown voltage Upr.max air (1) and neon (2) from the product of gas pressure R to the distance between the electrodes h

At sufficiently high frequencies, free electrons have time to shift by long distances and reach the electrodes. Ions with a large mass during the half-cycle of oscillations do not have time to shift over significant distances and the concentration of positive ions in the interelectrode space increases, leading to the appearance of a so-called “space charge”. Therefore, starting from frequencies exceeding tens of kilohertz, the probability of collisions of ions with molecules increases and the electrical strength of gases decreases (Figure 5.13). Further growth frequency of the electric field leads to the fact that during the half-cycle not only do the positive ions not have time to move over significant distances, but also the electrons do not have time to fly out of the interelectrode space. The probability of recombination of charged particles increases and their concentration decreases. In addition, reducing the half-cycle time requires increasing the force acting on the ions so that kinetic energy enough to ionize the molecules. Therefore, at frequencies exceeding one megahertz, the electrical strength of gases increases.

Rice. 5.13. Dependence of the electrical strength of gas on the frequency of the electric field

Breakdown of gas (air) in a non-uniform field preceded cop ion discharge or corona, which is an incomplete breakdown. Corona occurs when stressed U to, which is lower than U np (Uk< U np), near an electrode with a small radius of curvature, on sharp metal edges, etc.; it is observed in the form of an intermittent bluish glow and is accompanied by a characteristic sound (buzzing or crackling). As the voltage increases, the corona discharge turns into spark and then, with sufficient power of the voltage source - in arc discharge.

In the case of rod-plane electrodes, creating a sharply inhomogeneous field, U pr gases will be the smallest with a positive polarity of the rod and the largest with a negative polarity of the rod (Figure 5.14). This is explained as follows. As noted above, the breakdown of the air gap is preceded by a corona discharge. The electrons formed in this case, having a greater (~ 1000 times) mobility than positive ions, quickly leave the corona layer, and a bulk volume appears. positive charge. The volumetric positive charge formed near the tip of the electrode has a different effect on the voltage of the air gap. If there is a rod-shaped electrode positive potential, then the positive volume charge will lead to an increase in the field strength in the outer region of the corona, and breakdown will occur at a lower value U pr. If there is a negative potential on the rod, then the positive volume charge will reduce the field strength in the outer region of the corona, and breakdown of the air gap will occur at a higher value U ave. With decreasing pulse duration (increasing voltage frequency), the difference between the values U pr decreases depending on the polarity of the rod. Magnitude U pr during gas breakdown at high frequencies in a non-uniform field (as opposed to breakdown in a uniform field) is significantly lower than U pr at constant voltage or power frequency voltage.

Rice. 5.14. Dependence of breakdown voltage Uetc air from distance h

between electrodes (non-uniform field)

In inhomogeneous fields with increasing air humidity, breakdown voltage U pr increases. This can be explained by the increased ability of water molecules to capture free electrons and turn into sedentary electrons. negative ions. As a result, the number of ionizing electrons in the interelectrode space decreases, therefore the discharge voltage increases. It can be approximately assumed that when the absolute air humidity doubles U np at a frequency of 50 Hz it increases by 10%.

Surface discharge. If the electric field in the interelectrode space is uniform, then breakdown can occur anywhere and at the highest voltage. If a solid dielectric is introduced into a uniform field, as shown in Figure 5.15.a, then electrical discharge will occur in air over the surface of a solid dielectric and, other things being equal, at a lower voltage. In this case, the discharge voltage U p will depend on a number of factors and, first of all, on the physicochemical properties of the solid dielectric, the state of the sample surface and its location relative to the field lines, air humidity, the shape and frequency of the applied field, the tightness of the electrodes to the solid dielectric and the distance between them.

Rice. 5.15 Distribution of vector lines E in an electrical insulating structure consisting of a solid dielectric (1) and air (2):

a - field lines are directed parallel,

b - perpendicular to the dielectric interface

Dependency curves U p from distance L between electrodes in homogeneous and inhomogeneous electric fields depending on the nature of the solid dielectric (value dielectric constantε and specific surface electrical conductivity g s) are presented in Figure 5.16. The figure shows that with increasing distance between the electrodes U p increases unequally for solid dielectrics of different chemical natures. The highest U p observed during discharge along the surface of non-polar solid dielectrics molecular structure. For polar dielectrics U p lower than for non-polar ones, and the lower, the greater the ε and g s of the solid dielectric and the smaller its contact angle. In dielectrics ionic structure(see Figure 5.16. a), curves 3 and 4), which contain ions alkali metals and therefore have a higher surface electrical conductivity, U p even lower than that of polar dielectrics of molecular structure. Especially significantly U p decreases with poor adherence of electrodes to the surface solid dielectric (curve 5). In this case, the electric field in the interelectrode space becomes more inhomogeneous, as a result of which the discharge voltage decreases.

It has been established that on the surface of a solid dielectric a continuous or discontinuous film of moisture condensed from the air with a thickness of a monomolecular layer or more is formed, which violates the uniformity of the field, and therefore U p decreases. In this case, the electrical discharge actually occurs in a non-uniform field. Moreover, the greater the electrical conductivity of the water film, the lower U p.

Rice. 5.16. Discharge voltage dependence U p in the air along the surface of dielectrics from a distance L between electrodes in a uniform field (a) and a non-uniform field (b) and on the value of the dielectric constant ε( I) and specific surface electrical conductivity γ s (II) of a solid dielectric (c):

a, b - sample diameter 50 mm; 1 - paraffin, 2 - bakelite, 3 - porcelain, 4 - glass, 5 - porcelain and glass with poor electrode contact, 6 - air gap;

c - plane-parallel electrodes with rounded edges, sample diameter 45 mm, height 30 mm, T=20°C; U - PTFE, 2- PE, 3- PS, 4- PMMA, 5- vinyl plastic, b - wood, 7- getinax, 8- air gap

If the surface of a solid dielectric is very rough and contains cracks, then air microgaps are formed in these places, which are connected in series with the solid dielectric. Due to different values ​​of the dielectric constant of air and a solid dielectric, the field strength in the microgaps increases and, having reached the initial strength, causes ionization of air inclusions. Ionization, in turn, becomes an additional factor in increasing field inhomogeneity and reducing U p. To decline U p other factors also influence. It is known that there are always free positive and negative ions in the air. Therefore, on the surface of solid dielectrics, even in very dry air, a layer of ions of the same sign is formed, and above it, in the air, a layer of ions of the opposite sign is formed. Under the influence of an applied voltage, these ions, together with water ions, are displaced to oppositely charged electrodes, participating in the formation of space charges. The magnitude of the space charges formed at the electrodes is affected not only by the surface electrical conductivity, but also by the duration of the voltage. With short pulses and high frequencies (ƒ> 50 kHz), a small number of ions have time to shift, so the electric field is slightly distorted, and, therefore, U p decreases slightly.

Now we will take a qualitative look at some of the characteristics of the fields around conductors. Let's charge a conductor with electricity, but this time not a spherical one, but one that has a tip or edge (for example, in the shape shown in Fig. 6.14). Then the field in this place will be much stronger than in other places. The reason, in general terms, is that charges tend to spread as widely as possible over the surface of the conductor, and the tip of the point is always furthest from the rest of the surface. Therefore, part of the charges on the plate flows towards the tip. A relatively small amount of charge on it can create a high surface density, and a high density means a strong field near the conductor at that location.

Figure 6.14. The electric field at the sharp edge of the conductor is very high.

In general, in those places of the conductor in which the radius of curvature is smaller, the field is stronger. To see this, consider a combination of a large and a small sphere connected by a wire, as shown in Fig. 6.15. The wire itself will not greatly influence the external fields; his job is to equalize the potentials of the spheres. Near which ball will the field be more intense? If the radius of the left ball is , and the charge is , then its potential is approximately equal to

(Of course, the presence of one ball will affect the distribution of charges on the other, so that in fact none of them will have charges distributed symmetrically. But if we are only interested in the approximate magnitude of the field, then we can use the formula for the potential of a spherical charge.) If less a ball of radius has a charge, then its potential is approximately equal to

But, so

On the other hand, the field near the surface [see equation (5.8)] is proportional to the surface charge density, which in turn is proportional to the total charge divided by the square of the radius. It turns out that

(6.35)

Figure 6.15. The field of a pointed object can be approximately considered the field of two spheres of equal potential.

This means that the surface of the smaller sphere has a larger field. The fields are inversely proportional to the radii.

This result is very important from a technical point of view, because a breakdown occurs in the air if the field is too large. Any free charge in the air (an electron or an ion) is accelerated by this field, and if it is very strong, then the charge can gain such a speed before colliding with an atom that it will knock out a new electron from the atom. As a result, more and more ions appear. Their movement constitutes a spark, or discharge. If you want to charge a body to a high potential without it being discharged into the air, you must be sure that the surface of the body is smooth and that there are no places where the field is too high.

Now we will take a qualitative look at some of the characteristics of the fields around conductors. Let's charge a conductor with electricity, but this time not a spherical one, but one that has a tip or edge (for example, in the shape shown in Fig. 6.14). Then the field in this place will be much stronger than in other places. The reason, in general terms, is that charges tend to spread as widely as possible over the surface of the conductor, and the tip of the point is always furthest from the rest of the surface. Therefore, part of the charges on the plate flows towards the tip. Relatively small quantity charge on it can create a large surface density, and high density means a strong field near the conductor in this place.

Fig. 6.14. The electric field at the sharp edge of the conductor is very high.

IN In general, in those places of the conductor in which the radius of curvature is smaller, the field is stronger. To see this, consider a combination of a large and a small sphere connected by a wire, as shown in Fig. 6.15. The wire itself will not greatly influence the external fields; his job is to equalize the potentials of the spheres. Near which ball will the field be more intense? If the radius of the left ball is a, and the charge is Q, then its potential is approximately equal to

(Of course, the presence of one ball will affect the distribution of charges on the other, so that in fact none of them will have charges distributed symmetrically. But if we are only interested in the approximate magnitude of the field, then we can use the formula for the potential of a spherical charge.) If less ball of radius b has a charge q, then its potential is approximately equal

But  1 = 2, so

WITH on the other hand, the field near the surface [see equation (5.8)] is proportional to the surface charge density, which in turn is proportional to the total charge divided by the square of the radius. It turns out that

Fig. 6.15. The field of a pointed object can be approximately considered the field of two spheres of equal potential.

This means that the surface of the smaller sphere has a larger field. The fields are inversely proportional to the radii.

This result is very important from a technical point of view, because a breakdown occurs in the air if the field is too large. Any free charge in the air (an electron or an ion) is accelerated by this field, and if it is very strong, then the charge can gain such a speed before colliding with an atom that it will knock out a new electron from the atom. As a result, more and more ions appear. Their movement constitutes a spark, or discharge. If you want to charge a body to a high potential without it being discharged into the air, you must be sure that the surface of the body is smooth and that there are no places where the field is too high.

§ 12. Ion microscope

The ultra-high electric field surrounding any sharp protrusion of a charged conductor has received interesting application in one device. Job ion microscope caused by powerful fields arising around metal tip. This device is designed like this. A very thin needle, the tip diameter of which is no more than 1000 Å, is placed in the center of a glass sphere from which the air has been pumped out (Fig. 6.16). The inner surface of the sphere is coated with a thin conductive layer of fluorescent material, and a very high potential difference is created between the needle and the fluorescent coating.

Let's first see what happens if the needle is negatively charged in relation to the fluorescent screen. The field lines at the tip of the needle are very concentrated. The electric field can reach 40 10 6 V per 1 cm. In such strong fields, electrons are separated from the surface of the needle and accelerated in the area from the needle to the screen due to the potential difference. Having reached the screen, they cause a glow in this place (exactly like on the screen of a television tube).

Fig. 6.16. Ion microscope.

The electrons that came to this point fluorescent surface are, to a very good approximation, the same electrons that left the other end of the radial field line, because the electrons move along the field lines connecting the tip of the needle to the surface of the sphere. So on the surface we see a kind of image of the tip of a needle. Or rather, we see the picture emissivity tip surface, i.e. the ease with which electrons can leave the surface of the metal tip. If the resolution strength is high enough, then one can expect to resolve the provisions individual atoms at the tip of the needle. But with electrons such resolution cannot be achieved for the following reasons. First, quantum mechanical diffraction occurs electron waves, and the image will become blurred. Secondly, as a result of internal motion in the metal, electrons have a small transverse initial velocity at the moment they escape from the needle, and this random transverse component of the velocity will lead to smearing of the image. In total, these effects limit the resolution of details to about 25A.

If, however, we change the sign of the voltage and let a little helium into the flask, then the details will be better resolved. When a helium atom collides with the tip of the tip, a powerful field strips an electron from the atom and the atom becomes positively charged.

Fie.6 .17. Image obtained with an ion microscope.

The helium ion then accelerates along power line until it hits the screen. Since the helium ion is incomparably heavier than the electron, its quantum mechanical wavelengths are much shorter. And if, moreover, the temperature is not very high, then the influence of thermal velocities is also much weaker than that of an electron. The image is blurred less and a much sharper image of the needle tip is obtained. With a microscope operating on the principle of ion emission, it was possible to achieve magnification up to 2,000,000 times, i.e. ten times better than the best electron microscopes.

In fig. Figure 6.17 shows what was achieved on such a microscope using a tungsten needle. The centers of tungsten atoms ionize helium atoms slightly differently than the spaces between tungsten atoms. The location of the spots on the fluorescent screen demonstrates the arrangement individual atoms on a tungsten tip. Why the spots look like rings can be understood if you imagine a large box filled with balls laid in a rectangular grid and thus forming a cubic lattice. These balls are like atoms in metal. If you cut out a roughly spherical part from this box, you will see a pattern of rings characteristic of atomic structure. The ion microscope provided humanity with the first means of seeing atoms. A remarkable achievement, and even achieved with such a simple device.

*Cm. Muller's article [E. W. Mueller , The field-ion microscope, Advances in Electronics and Electron Physics, 13, 83 (I960)].