Control questions .. 18

9. Laboratory work No. 2. Study of thermionic emission at low emission current densities . 18

Work order .. 19

Report requirements . 19

Control questions .. 19

Introduction

Emission electronics studies phenomena associated with the emission (emission) of electrons from a condensed medium. Electron emission occurs in cases when part of the electrons of a body acquires, as a result of external influence, energy sufficient to overcome the potential barrier at its boundary, or if an external electric field makes it “transparent” to part of the electrons. Depending on the nature of the external influence, there are:

thermionic emission (heating of bodies);
secondary electron emission (bombardment of the surface with electrons);
ion-electron emission (bombardment of the surface with ions);
photoelectron emission (electromagnetic irradiation);
exoelectronic emission (mechanical, thermal and other types of surface treatment);
field emission (external electric field), etc.

In all phenomena where it is necessary to take into account either the exit of an electron from a crystal into the surrounding space, or the transition from one crystal to another, the characteristic called “Work function” acquires decisive significance. The work function is defined as the minimum energy required to remove an electron from a solid and place it at a point where its potential energy is assumed to be zero. In addition to describing various emission phenomena, the concept of work function plays an important role in explaining the occurrence of a contact potential difference in the contact of two metals, a metal with a semiconductor, two semiconductors, as well as galvanic phenomena.

The guidelines consist of two parts. The first part contains basic theoretical information on emission phenomena in solids. The main attention is paid to the phenomenon of thermionic emission. The second part provides a description of laboratory work devoted to the experimental study of thermionic emission, the study of contact potential difference and the distribution of work function over the surface of the sample.

Part 1. Basic theoretical information

1. Electron work function. Influence on the work function of the surface state

The fact that electrons are retained inside a solid indicates that a retarding field arises in the surface layer of the body, preventing electrons from leaving it into the surrounding vacuum. A schematic representation of a potential barrier at the boundary of a solid is shown in Fig. 1. To leave the crystal, an electron must do work equal to the work function. Distinguish thermodynamic And external work function.

The thermodynamic work function is the difference between the zero-level energy of vacuum and the Fermi energy of a solid.

External work function (or electron affinity) is the difference between the energy of the zero vacuum level and the energy of the bottom of the conduction band (Fig. 1).

Rice. 1. Form of crystal potential U along the line of location of ions in the crystal and in the near-surface region of the crystal: the positions of the ions are marked by dots on the horizontal line; φ=- U /е – work function potential; E F – Fermi energy (negative); E C– energy of the bottom of the conduction band; W O – thermodynamic work function; W a – external work function; the shaded area conventionally represents filled electronic states

There are two main reasons for the emergence of a potential barrier at the boundary of a solid and vacuum. One of them is due to the fact that an electron emitted from a crystal induces a positive electric charge on its surface. An attractive force arises between the electron and the surface of the crystal (electric image force, see Section 5, Fig. 12), tending to return the electron back to the crystal. Another reason is due to the fact that electrons, due to thermal motion, can cross the surface of the metal and move away from it to short distances (on the order of atomic). They form a negatively charged layer above the surface. In this case, after the electrons escape, a positively charged layer of ions is formed on the surface of the crystal. As a result, an electrical double layer is formed. It does not create a field in external space, but it also requires work to overcome the electric field inside the double layer itself.

The work function value for most metals and semiconductors is several electron volts. For example, for lithium the work function is 2.38 eV, iron – 4.31 eV, germanium – 4.76 eV, silicon – 4.8 eV. To a large extent, the work function value is determined by the crystallographic orientation of the single crystal face from which electron emission occurs. For the (110) plane of tungsten, the work function is 5.3 eV; for the (111) and (100) planes these values are 4.4 eV and 4.6 eV, respectively.

Thin layers deposited on the surface of the crystal have a great influence on the work function. Atoms or molecules deposited on the surface of a crystal often donate an electron to it or accept an electron from it and become ions. In Fig. Figure 2 shows the energy diagram of a metal and an isolated atom for the case when the thermodynamic work function of an electron from the metal W 0 greater than ionization energy E ion of an atom deposited on its surface. In this situation, the electron of the atom is energetically favorable tunnel into the metal and descend in it to the Fermi level. The metal surface covered with such atoms becomes negatively charged and forms a double electric layer with positive ions, the field of which will reduce the work function of the metal. In Fig. 3, a shows a tungsten crystal coated with a monolayer of cesium. Here the situation discussed above is realized, since the energy E ion cesium (3.9 eV) is less than the work function of tungsten (4.5 eV). In experiments, the work function decreases by more than three times. The opposite situation is observed if tungsten is covered with oxygen atoms (Fig. 3 b). Since the bond of valence electrons in oxygen is stronger than in tungsten, when oxygen is adsorbed on the surface of tungsten, an electric double layer is formed, which increases the work function of the metal. The most common case is when an atom deposited on the surface does not completely give up its electron to the metal or takes in an extra electron, but deforms its electron shell so that the atoms adsorbed on the surface are polarized and become electric dipoles (Fig. 3c). Depending on the orientation of the dipoles, the work function of the metal decreases (the orientation of the dipoles corresponds to Fig. 3c) or increases.

2. Thermionic emission phenomenon

Thermionic emission is one of the types of electron emission from the surface of a solid. In the case of thermionic emission, the external influence is associated with heating of the solid.

The phenomenon of thermionic emission is the emission of electrons by heated bodies (emitters) into a vacuum or other medium.

Under thermodynamic equilibrium conditions, the number of electrons n(E), having energy in the range from E before E+d E, is determined by the Fermi-Dirac statistics:

,(1)

Where g(E)– number of quantum states corresponding to energy E; E F – Fermi energy; k– Boltzmann constant; T– absolute temperature.

In Fig. Figure 4 shows the energy diagram of the metal and the electron energy distribution curves at T=0 K, at low temperature T 1 and at high temperatures T 2. At 0 K, the energy of all electrons is less than the Fermi energy. None of the electrons can leave the crystal and no thermionic emission is observed. With increasing temperature, the number of thermally excited electrons capable of leaving the metal increases, which causes the phenomenon of thermionic emission. In Fig. 4 this is illustrated by the fact that when T=T 2 the "tail" of the distribution curve goes beyond the zero level of the potential well. This indicates the appearance of electrons with energy exceeding the height of the potential barrier.

For metals, the work function is several electron volts. Energy k T even at temperatures of thousands of Kelvin is a fraction of an electron volt. For pure metals, significant electron emission can be obtained at a temperature of about 2000 K. For example, in pure tungsten, noticeable emission can be obtained at a temperature of 2500 K.

To study thermionic emission, it is necessary to create an electric field at the surface of a heated body (cathode), accelerating electrons to remove them (suction) from the emitter surface. Under the influence of an electric field, the emitted electrons begin to move and an electric current is formed, which is called thermionic. To observe thermionic current, a vacuum diode is usually used - an electron tube with two electrodes. The cathode of the lamp is a filament made of a refractory metal (tungsten, molybdenum, etc.), heated by an electric current. The anode usually has the shape of a metal cylinder surrounding a heated cathode. To observe thermionic current, the diode is connected to the circuit shown in Fig. 5. Obviously, the strength of the thermionic current should increase with increasing potential difference V between the anode and cathode. However, this increase is not proportional V(Fig. 6). Upon reaching a certain voltage, the increase in thermionic current practically stops. The limiting value of the thermionic current at a given cathode temperature is called the saturation current. The magnitude of the saturation current is determined by the number of thermionic electrons that are able to exit the cathode surface per unit time. In this case, all the electrons supplied by thermionic emission from the cathode are used to produce an electric current.

3. Dependence of thermionic current on temperature. Formula Richardson-Deshman

When calculating the thermionic current density we will use the electron gas model and apply Fermi-Dirac statistics to it. It is obvious that the thermionic current density is determined by the density of the electron cloud near the crystal surface, which is described by formula (1). In this formula, let us move from the energy distribution of electrons to the electron momentum distribution. In this case, we take into account that the allowed values of the electron wave vector k V k -space are distributed evenly so that for each value k accounted for volume 8 p 3 (for a crystal volume equal to one). Considering that the electron momentum p =ћ k we obtain that the number of quantum states in the volume element of momentum space dp xdp ydp z will be equal

(2)

The two in the numerator of formula (2) takes into account two possible values of the electron spin.

Let's direct the axis z rectangular coordinate system normal to the cathode surface (Fig. 7). Let us select an area of unit area on the surface of the crystal and build on it, as on a base, a rectangular parallelepiped with a side edge v z =p z /m n(m n– effective electron mass). Electrons contribute to the saturation current density of the component v z axis speed z. The contribution to the current density from one electron is equal to

(3)

Where e– electron charge.

The number of electrons in the parallelepiped, the velocities of which are contained in the considered interval:

In order for the crystal lattice not to be destroyed during the emission of electrons, an insignificant part of the electrons must leave the crystal. For this, as formula (4) shows, the condition must be satisfied HERF>> k T. For such electrons, unity in the denominator of formula (4) can be neglected. Then this formula is transformed to the form

(5)

Let us now find the number of electrons dN in the scope under consideration, z-the impulse component of which is contained between R z And R z +dp z. To do this, the previous expression must be integrated over R x And R y ranging from –∞ to +∞. When integrating, it should be taken into account that

and use the table integral

As a result we get

.(6)

Now, taking into account (3), let us find the density of the thermionic current created by all the electrons of the parallelepiped. To do this, expression (6) must be integrated for all electrons whose kinetic energy is at the Fermi level E ≥E F +W 0 Only such electrons can leave the crystal and only they play a role in calculating the thermocurrent. The component of the momentum of such electrons along the axis Z must satisfy the condition

Therefore, the saturation current density

Integration is performed for all values. Let us introduce a new integration variable

Then p z dp z =m n du And

.(8)

As a result we get

,(9)

,(10)

where is the constant

Equality (10) is called the formula Richardson-Deshman. By measuring the density of the thermionic saturation current, one can use this formula to calculate the constant A and the work function W 0 . For experimental calculations, the formula Richardson-Deshman it is convenient to represent it in the form

In this case, the graph shows the dependence ln(js/T 2) from 1 /T expressed by a straight line. From the intersection of the straight line with the ordinate axis, ln is calculated A , and by the angle of inclination of the straight line the work function is determined (Fig. 8).

4. Contact potential difference

Let us consider the processes that occur when two electronic conductors, for example two metals, with different work functions approach and come into contact. The energy diagrams of these metals are shown in Fig. 9. Let EF 1 And EF 2 is the Fermi energy for the first and second metal, respectively, and W 01 And W 02– their work functions. In an isolated state, metals have the same vacuum level and, therefore, different Fermi levels. Let us assume for definiteness that W 01< W 02, then the Fermi level of the first metal will be higher than that of the second (Fig. 9 a). When these metals come into contact opposite the occupied electronic states in metal 1, there are free energy levels of metal 2. Therefore, when these conductors come into contact, a resulting flow of electrons arises from conductor 1 to conductor 2. This leads to the fact that the first conductor, losing electrons, becomes positively charged, and second conductor, acquiring additional negative charge is charged negatively. Due to charging, all energy levels of metal 1 shift down, and metal 2 shifts up. The process of level displacement and the process of electron transition from conductor 1 to conductor 2 will continue until the Fermi levels of both conductors are aligned (Fig. 9 b). As can be seen from this figure, the equilibrium state corresponds to the potential difference between the zero levels of conductors 0 1 and 0 2:

.(11)

Potential difference V K.R.P called contact potential difference. Consequently, the contact potential difference is determined by the difference in the work function of electrons from the contacting conductors. The obtained result is valid for any methods of exchanging electrons between two materials, including by thermionic emission in a vacuum, through an external circuit, etc. Similar results are obtained when metal contacts a semiconductor. A contact potential difference arises between the metals and the semiconductor, which is approximately the same order of magnitude as in the case of contact between two metals (approximately 1 V). The only difference is that if in conductors the entire contact potential difference falls almost on the gap between the metals, then when a metal comes into contact with a semiconductor, the entire contact potential difference falls on the semiconductor, in which a sufficiently large layer is formed, enriched or depleted of electrons. If this layer is depleted of electrons (in the case when the work function of an n-type semiconductor is less than the work function of the metal), then such a layer called blocking and such a transition will have straightening properties. The potential barrier that arises in the rectifying contact of a metal with a semiconductor is called Schottky barrier, and diodes operating on its basis - Schottky diodes.

Volt-ampereCharacteristics of a thermionic cathode at low emission current densities. Schottky effect

If a potential difference is created between the thermionic cathode and the anode of the diode (Fig. 5) V, preventing the movement of electrons to the anode, then only those that fly out from the cathode with a reserve of kinetic energy not less than the energy of the electrostatic field between the anode and the cathode will be able to reach the anode, i.e. -e V(V< 0). To do this, their energy in the thermionic cathode must be no less W 0 –еV. Then, replacing in the formula Richardson-Deshman (10) W 0 on W 0 –еV, we obtain the following expression for the thermal emission current density:

,(12)

Here j S– saturation current density. Let's take logarithm of this expression

.(13)

At a positive potential at the anode, all electrons leaving the thermionic cathode land on the anode. Therefore, the current in the circuit should not change, remaining equal to the saturation current. Thus, volt-ampere The characteristic (current-voltage characteristic) of the thermal cathode will have the form shown in Fig. 10 (curve a).

A similar current-voltage characteristic is observed only at relatively low emission current densities and high positive potentials at the anode, when a significant electron space charge does not arise near the emitting surface. Current-voltage characteristics of the thermionic cathode taking into account the space charge, discussed in Section. 6.

Let us note another important feature of the current-voltage characteristic at low emission current densities. The conclusion is that the thermocurrent reaches saturation at V=0, is valid only for the case when the cathode and anode materials have the same thermodynamic work function. If the work functions of the cathode and anode are not equal, then a contact potential difference appears between the anode and cathode. In this case, even in the absence of an external electric field ( V=0) there is an electric field between the anode and cathode due to the contact potential difference. For example, if W 0k< W 0a then the anode will be charged negatively relative to the cathode. To destroy the contact potential difference, a positive bias should be applied to the anode. That's why volt-ampere the characteristic of the hot cathode shifts by the amount of the contact potential difference towards the positive potential (Fig. 10, curve b). With an inverse relationship between W 0k And W 0a the direction of the shift of the current-voltage characteristic is opposite (curve c in Fig. 10).

Conclusion about the independence of the saturation current density at V>0 is highly idealized. In real current-voltage characteristics of thermionic emission, a slight increase in thermionic emission current is observed with increasing V in saturation mode, which is associated with Schottky effect(Fig. 11).

The Schottky effect is a decrease in the work function of electrons from solids under the influence of an external accelerating electric field.

To explain the Schottky effect, consider the forces acting on an electron near the surface of a crystal. In accordance with the law of electrostatic induction, surface charges of the opposite sign are induced on the surface of the crystal, which determine the interaction of the electron with the surface of the crystal. In accordance with the method of electrical images, the action of real surface charges on an electron is replaced by the action of a fictitious point positive charge +e, located at the same distance from the crystal surface as the electron, but on the opposite side of the surface (Fig. 12). Then, in accordance with Coulomb's law, the force of interaction between two point charges

,(14)

Here ε o– electrical constant: X is the distance between the electron and the surface of the crystal.

The potential energy of an electron in the electric image force field, if counted from the zero vacuum level, is equal to

.(15)

Potential energy of an electron in an external accelerating electric field E

Total potential energy of an electron

.(17)

A graphical determination of the total energy of an electron located near the surface of the crystal is shown in Fig. 13, which clearly shows a decrease in the work function of an electron from the crystal. The total electron potential energy curve (solid curve in Fig. 13) reaches a maximum at the point x m:

.(18)

This point is 10 Å from the surface at an external field strength » 3× 10 6 V/cm.

At the point X m total potential energy equal to the decrease in the potential barrier (and, therefore, the decrease in the work function),

.(19)

As a result of the Schottky effect, the thermal diode current at a positive voltage at the anode increases with increasing anode voltage. This effect manifests itself not only when electrons are emitted into a vacuum, but also when they move through metal-semiconductor or metal-insulator contacts.

6. Currents in vacuum limited by space charge. The law of "three second"

At high thermionic emission current densities, the current-voltage characteristic is significantly influenced by the volumetric negative charge that arises between the cathode and anode. This negative bulk charge prevents electrons escaping from the cathode from reaching the anode. Thus, the anode current turns out to be less than the electron emission current from the cathode. When a positive potential is applied to the anode, the additional potential barrier at the cathode created by the space charge decreases and the anode current increases. This is a qualitative picture of the influence of space charge on the current-voltage characteristic of a thermal diode. This issue was theoretically explored by Langmuir in 1913.

Let us calculate, under a number of simplifying assumptions, the dependence of the thermal diode current on the external potential difference applied between the anode and cathode and find the distribution of the field, potential and electron concentration between the anode and cathode, taking into account the space charge.

Rice. 14. To the conclusion of the law of "three second"

Let's assume that the diode electrodes are flat. With a small distance between the anode and cathode d they can be considered infinitely large. We place the origin of coordinates on the surface of the cathode, and the axis X Let's direct it perpendicular to this surface towards the anode (Fig. 14). We will maintain the cathode temperature constant and equal T. Electrostatic field potential j , existing in the space between the anode and cathode, will be a function of only one coordinate X. He must satisfy Poisson's equation

,(20)

Here r – volumetric charge density; n– electron concentration; j , r And n are functions of the coordinate X.

Considering that the current density between the cathode and anode

and the electron speed v can be determined from the equation

Where m– electron mass, equation (20) can be transformed to the form

, .(21)

This equation must be supplemented with boundary conditions

These boundary conditions follow from the fact that the potential and electric field strength at the cathode surface must vanish. Multiplying both sides of equation (21) by dj /dx, we get

.(23)

Considering that

(24a)

And ,(24b)

we write (23) in the form

.(25)

Now we can integrate both sides of equation (25) over X ranging from 0 to that value x, at which the potential is equal j . Then, taking into account boundary conditions (22), we obtain

Integrating both parts (27) ranging from X=0, j =0 to X=1, j= V a, we get

.(28)

By squaring both sides of equality (28) and expressing the current density j from A according to (21), we get

.(30)

Formula (29) is called Langmuir's "three-second law".

This law is valid for electrodes of arbitrary shape. The expression for the numerical coefficient depends on the shape of the electrodes. The formulas obtained above make it possible to calculate the distributions of potential, electric field strength and electron density in the space between the cathode and anode. Integration of expression (26) ranging from X=0 to the value when the potential is equal j , leads to the relation

those. the potential varies proportionally to the distance from the cathode X to the power of 4/3. Derivative dj/ dx characterizes the electric field strength between the electrodes. According to (26), the magnitude of the electric field strength E ~X 19 . Finally, the electron concentration

(32)

and, according to (31) n(x)~ (1/x) 2/9 .

Dependencies j (X ), E(X) And n(X) are shown in Fig. 15. If X→0, then the concentration tends to infinity. This is a consequence of neglecting the thermal velocities of electrons at the cathode. In a real situation, during thermionic emission, electrons leave the cathode not with zero speed, but with a certain finite emission speed. In this case, the anode current will exist even if there is a small reverse electric field near the cathode. Consequently, the volume charge density can change to such values that the potential near the cathode decreases to negative values (Fig. 16). As the anode voltage increases, the minimum potential decreases and approaches the cathode (curves 1 and 2 in Fig. 16). At a sufficiently high voltage at the anode, the minimum potential merges with the cathode, the field strength at the cathode becomes zero and the dependence j (X) approaches (29), calculated without taking into account the initial electron velocities (curve 3 in Fig. 16). At high anodic voltages, the space charge is almost completely dissolved and the potential between the cathode and anode changes according to a linear law (curve 4, Fig. 16).

Thus, the potential distribution in the interelectrode space, taking into account the initial electron velocities, differs significantly from that which is the basis of the idealized model when deriving the “three second” law. This leads to a change and dependence of the anode current density. Calculation taking into account the initial electron velocities for the case of the potential distribution shown in Fig. 17, and for cylindrical electrodes gives the following dependence for the total thermionic emission current I (I=jS, Where S– cross-sectional area of the thermocurrent):

.(33)

Options x m And V m determined by the type of dependence j (X), their meaning is clear from Fig. 17. Parameter X m equal to the distance from the cathode at which the potential reaches its minimum value = V m. Factor C(x m), except x m, depends on the radii of the cathode and anode. Equation (33) is valid for small changes in the anode voltage, because And X m And V m, as discussed above, depend on the anode voltage.

Thus, the law of the “three second” is not universal; it is valid only in a relatively narrow range of voltages and currents. However, it is a clear example of the nonlinear relationship between current and voltage in an electronic device. The nonlinearity of the current-voltage characteristic is the most important feature of many elements of radio and electrical circuits, including elements of solid-state electronics.

Part 2. Laboratory work

7. Experimental setup for studying thermionic emission

Laboratory work No. 1 and 2 is performed on one laboratory installation, implemented on the basis of a universal laboratory stand. The installation diagram is shown in Fig. 18. The measuring section contains an EL vacuum diode with a directly or indirectly heated cathode. The front panel of the measuring section displays the contacts of the filament “Incandescent”, the anode “Anode” and the cathode “Cathode”. The filament source is a stabilized direct current source of type B5-44A. The I icon in the diagram indicates that the source operates in current stabilization mode. The procedure for working with a direct current source can be found in the technical description and operating instructions for this device. Similar descriptions are available for all electrical measuring instruments used in laboratory work. The anode circuit includes a stabilized direct current source B5-45A and a universal digital voltmeter B7-21A, used in the direct current measurement mode to measure the anode current of the thermal diode. To measure the anode voltage and cathode heating current, you can use devices built into the power source or connect an additional voltmeter RV7-32 for a more accurate measurement of the voltage at the cathode.

The measuring section may contain vacuum diodes with different working cathode filament currents. At the rated filament current, the diode operates in the mode of limiting the anode current by space charge. This mode is necessary to perform laboratory work No. 1. Laboratory work No. 2 is performed at reduced filament currents, when the influence of space charge is insignificant. When setting the filament current, you should be especially careful, because Excess of the filament current above its nominal value for a given vacuum tube leads to burnout of the cathode filament and failure of the diode. Therefore, when preparing for work, be sure to check with your teacher or engineer the value of the operating filament current of the diode used in the work; be sure to write down the data in your workbook and use it when drawing up a report on laboratory work.

8. Laboratory work No. 1. Studying the influence of space charge on volt-amperethermal current characteristics

Purpose of the work: experimental study of the dependence of thermionic emission current on the anode voltage, determination of the exponent in the “three-second” law.

Volt-ampere The characteristic of thermionic emission current is described by the law of “three second” (see Section 6). This mode of diode operation occurs at sufficiently high cathode filament currents. Typically, at rated filament current, the vacuum diode current is limited by space charge.

The experimental setup for performing this laboratory work is described in Sect. 7. During work, it is necessary to measure the current-voltage characteristic of the diode at the rated filament current. The value of the operating current scale of the vacuum tube used should be taken from a teacher or engineer and written down in a workbook.

Work order

1. Familiarize yourself with the description and procedure for operating the instruments necessary for the operation of the experimental setup. Assemble the circuit according to Fig. 18. The installation can be connected to the network only after checking the correctness of the assembled circuit by an engineer or teacher.

2. Turn on the cathode filament current power supply and set the required filament current. Since when the filament current changes, the temperature and resistance of the filament changes, which, in turn, leads to a change in the filament current, adjustment must be carried out using the method of successive approximations. After completing the adjustment, you must wait approximately 5 minutes for the filament current and cathode temperature to stabilize.

3. Connect a constant voltage source to the anode circuit and, by changing the voltage at the anode, measure the current-voltage characteristic point by point. Take the current-voltage characteristic in the range 0...25 V, every 0.5...1 V.

Ia(V a), Where Ia– anode current, V a– anode voltage.

5. If the range of changes in the anode voltage is taken to be small, then the values x m, C(x,n) And V m, included in formula (33), can be taken constant. At large V a size V m can be neglected. As a result, formula (33) is transformed to the form (after transition from the thermocurrent density j to its full value I)

6. From formula (34) determine the value WITH for three maximum values of the anode voltage on the current-voltage characteristic. Calculate the arithmetic mean of the obtained values. Substituting this value into formula (33), determine the value V m for three minimum voltage values at the anode and calculate the arithmetic mean value V m.

7. Using the obtained value V m, plot the dependence of ln Ia from ln( V a+|V m|). Determine the degree of dependence from the tangent of the angle of this graph Ia(V a + V m). It should be close to 1.5.

8. Prepare a report on the work.

Report requirements

5. Conclusions on the work.

Control questions

1. What is the phenomenon of thermionic emission called? Define the work function of an electron. What is the difference between thermodynamic and external work function?

2. Explain the reasons for the emergence of a potential barrier at the solid-vacuum boundary.

3. Explain, based on the energy diagram of the metal and the electron energy distribution curve, the thermal emission of electrons from the metal.

4. Under what conditions is thermionic current observed? How can you observe thermionic current? How does the thermal diode current depend on the applied electric field?

5. State the law Richardson-Deshman

6. Explain the qualitative picture of the influence of a negative volume charge on the current-voltage characteristic of a thermal diode. Formulate Langmuir's "three second" law.

7. What are the distributions of potential, electric field strength and electron density in the space between the cathode and anode at currents limited by space charge?

8. What is the dependence of the thermal emission current on the voltage between the anode and cathode, taking into account the space charge and initial electron velocities? Explain the meaning of the parameters that determine this dependence;

9. Explain the design of the experimental setup for studying thermionic emission. Explain the purpose of individual elements of the circuit.

10. Explain the method for experimentally determining the exponent in the law of “three-seconds”.

9. Laboratory work No. 2. Study of thermionic emission at low emission current densities

Purpose of the work: to study the current-voltage characteristics of a thermal diode at a low cathode heating current. Determination from experimental results of the contact potential difference between the cathode and anode, the cathode temperature.

At low thermal current densities volt-ampere the characteristic has a characteristic appearance with an inflection point corresponding to the modulus of the contact potential difference between the cathode and anode (Fig. 10). The cathode temperature can be determined as follows. Let us proceed to equation (12), which describes the current-voltage characteristic of thermionic emission at low current densities, from the thermocurrent density j to its full value I(j=I/S, Where S– cross-sectional area of the thermocurrent). Then we get

Where I S– saturation current.

Taking logarithms of (35), we have

.(36)

To the extent that equation (36) describes the current-voltage characteristic in the area to the left of the inflection point, then to determine the cathode temperature it is necessary to take any two points in this area with anode currents I a 1, I a 2 and anode voltages U a 1, U a 2 respectively. Then, according to equation (36),

From here we obtain the working formula for the cathode temperature

.(37)

Work order

To perform laboratory work you must:

2. Turn on the cathode filament current power supply and set the required filament current. After setting the current, you must wait approximately 5 minutes for the filament current and cathode temperature to stabilize.

3. Connect a constant voltage source to the anode circuit and, by changing the voltage at the anode, measure the current-voltage characteristic point by point. Volt-ampere take the characteristic in the range of 0...5 V every 0.05...0.2 V.

4. Present the measurement results on a graph in ln coordinates Ia(V a), Where Ia– anode current, V a– anode voltage. Since in this work the contact potential difference is determined graphically, the scale along the horizontal axis should be chosen so that the accuracy of determination V K.R.P was not less than 0.1 V.

5. Using the inflection point of the current-voltage characteristic, determine the contact potential difference between the anode and cathode.

6. Determine the cathode temperature for three pairs of points on the inclined linear section of the current-voltage characteristic to the left of the inflection point. The cathode temperature should be calculated using formula (37). Calculate the average temperature from these data.

7. Prepare a report on the work.

Report requirements

The report is drawn up on a standard sheet of A4 paper and must contain:

1. Basic information on the theory.

2. Diagram of the experimental setup and its brief description.

3. Results of measurements and calculations.

4. Analysis of the obtained experimental results.

5. Conclusions on the work.

Control questions

1. List the types of electron emission. What causes the release of electrons in each type of electron emission?

2. Explain the phenomenon of thermionic emission. Define the work function of an electron from a solid. How can we explain the existence of a potential barrier at the solid-vacuum boundary?

3. Explain, based on the energy diagram of the metal and the electron energy distribution curve, the thermal emission of electrons from the metal.

4. State the law Richardson-Deshman. Explain the physical meaning of the quantities included in this law.

5. What are the features of the current-voltage characteristics of the thermionic cathode at low emission current densities? How does the contact potential difference between the cathode and anode affect it?

6. What is the Schottky effect? How is this effect explained?

7. Explain the decrease in the potential barrier for electrons under the influence of an electric field.

8. How will the cathode temperature be determined in this lab?

9. Explain the method for determining the contact potential difference in this work.

10. Explain the diagram and purpose of individual elements of the laboratory setup.

Conduction electrons do not spontaneously leave the metal in appreciable quantities. This is explained by the fact that metal represents a potential hole for them. Only those electrons whose energy is sufficient to overcome the potential barrier present on the surface are able to leave the metal. The forces causing this barrier have the following origin. The random removal of an electron from the outer layer of positive ions of the lattice results in the appearance of an excess positive charge in the place where the electron left.

The Coulomb interaction with this charge forces the electron, whose speed is not very high, to return back. Thus, individual electrons constantly leave the surface of the metal, move away from it several interatomic distances and then turn back. As a result, the metal is surrounded by a thin cloud of electrons. This cloud, together with the outer layer of ions, forms an electric double layer (Fig. 60.1; circles - ions, black dots - electrons). The forces acting on the electron in such a layer are directed into the metal.

The work done against these forces when transferring an electron from the metal outward increases the potential energy of the electron

Thus, the potential energy of valence electrons inside the metal is less than outside the metal by an amount equal to the depth of the potential well (Fig. 60.2). The energy change occurs over a length of the order of several interatomic distances, so the walls of the well can be considered vertical.

The potential energy of an electron and the potential of the point at which the electron is located have opposite signs. It follows that the potential inside the metal is greater than the potential in the immediate vicinity of its surface (we will simply say “on the surface” for brevity) by the amount

Giving the metal an excess positive charge increases the potential both on the surface and inside the metal. The potential energy of the electron decreases accordingly (Fig. 60.3, a).

Let us recall that the values of potential and potential energy at infinity are taken as the reference point. The message of negative charge lowers the potential inside and outside the metal. Accordingly, the potential energy of the electron increases (Fig. 60.3, b).

The total energy of an electron in a metal consists of potential and kinetic energies. In § 51 it was found that at absolute zero the values of the kinetic energy of conduction electrons range from zero to the energy Emax coinciding with the Fermi level. In Fig. 60.4, the energy levels of the conduction band are inscribed in the potential well (the dotted line shows unoccupied levels). To be removed from the metal, different electrons must be given different energies.

Thus, an electron located at the lowest level of the conduction band must be given energy; for an electron located at the Fermi level, energy is sufficient

The minimum energy that must be imparted to an electron in order to remove it from a solid or liquid into a vacuum is called the work function. The work function is usually denoted by where Ф is a quantity called the output potential.

In accordance with the above, the work function of an electron from a metal is determined by the expression

We obtained this expression under the assumption that the metal temperature is 0 K. At other temperatures, the work function is also determined as the difference between the depth of the potential well and the Fermi level, i.e., definition (60.1) is extended to any temperature. The same definition applies to semiconductors.

The Fermi level depends on temperature (see formula (52.10)). In addition, due to the change in average distances between atoms due to thermal expansion, the depth of the potential well changes slightly. This leads to the fact that the work function is slightly dependent on temperature.

The work function is very sensitive to the state of the metal surface, in particular to its cleanliness. By selecting the proper surface coating, the work function can be greatly reduced. For example, applying a layer of alkaline earth metal oxide (Ca, Sr, Ba) to the surface of tungsten reduces the work function from 4.5 eV (for pure W) to 1.5-2.

PHYSICS

Law of conservation of charge. Coulomb's law. Dielectric constant of a substance.

Law of conservation of electric charge states that the algebraic sum of charges in an electrically closed system is conserved.

The law of conservation of charge in integral form:

Here Ω is some arbitrary region in three-dimensional space, is the boundary of this region, ρ is the charge density, and is the current density (electric charge flux density) across the boundary.

The law of conservation of charge in differential form:

Law of conservation of charge in electronics:

Kirchhoff's rules for currents follow directly from the law of conservation of charge. The combination of conductors and radio-electronic components is presented as an open system. The total influx of charges into a given system is equal to the total output of charges from the system. Kirchhoff's rules assume that an electronic system cannot significantly change its total charge.

Coulomb's law. The modulus of the force of interaction between two point charges in a vacuum is directly proportional to the product of the moduli of these charges and inversely proportional to the square of the distance between them. where is the force with which charge 1 acts on charge 2; q1,q2 - magnitude of charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in absolute value, to the distance between charges - r12); k - proportionality coefficient. Thus, the law indicates that like charges repel (and unlike charges attract).

Dielectric constant of a substance. A physical quantity equal to the ratio of the modulus of the external electric field strength in a vacuum to the modulus of the total field strength in a homogeneous dielectric is called the dielectric constant of a substance.

Electric field. Electric field strength. Electric field superposition method.

Electric field - one of the components of the electromagnetic field; a special type of matter that exists around bodies or particles with an electric charge, as well as in free form when the magnetic field changes (for example, in electromagnetic waves). The electric field is directly invisible, but can be observed due to its forceful effect on charged bodies.

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 test charge placed at a given point in the field to the value of this charge q: .

Electric field superposition method. If the field is formed not by one charge, but by several, then the forces acting on the test charge add up according to the rule of vector addition. Therefore, the strength of the system of charges at a given point, the field, is equal to the vector sum of the field strengths from each charge separately.

Electric field strength vector flow. Electrical bias. Ostrogradsky-Gauss theorem.

electric field strength across a given surface

the sum of flows through all areas into which the surface is divided

Electrical bias. Due to the different polarizability of dissimilar dielectrics, the field strengths in them will be different. Therefore, the number of power lines in each dielectric is also different.

Some of the lines emanating from charges surrounded by a closed surface will end at the dielectric interface and will not penetrate this surface. This difficulty can be eliminated by introducing into consideration a new physical characteristic of the field - the electric displacement vector

The vector is directed in the same direction as. The concept of vector lines and displacement flux is similar to the concept of field lines and tension flux dN0= DdScos(α)

Ostrogradsky formula - a formula that expresses the flow of a vector field through a closed surface by the integral of the divergence (how far the incoming and outgoing flow diverge) of this field over the volume limited by this surface: that is, the integral of the divergence of a vector field extended over a certain volume T is equal to the flux of the vector through the surface S bounding this volume.

Application of Gauss's theorem to the calculation of some electric fields in vacuum.

a) Field of an infinitely long thread

modulus of the field strength created by a uniformly charged infinitely long thread at a distance R from it,

b) field of a uniformly charged infinite plane

Let σ be the surface charge density on the plane

c) the field of two uniformly charged opposite planes

d) field of a uniformly charged spherical surface

Electric field potential. Potential nature of electric fields.

Electrostatic potential (see also Coulomb potential) - a scalar energy characteristic of an electrostatic field, characterizing the potential energy of the field possessed by a unit charge placed at a given point in the field. Electrostatic potential is equal to the ratio of the potential energy of interaction of a charge with a field to the magnitude of this charge: J/C

Potential nature of electric fields.

The interaction between stationary charges is carried out through an electrostatic field: it is not the charges that interact, but one charge at its location interacts with the field created by another charge. This is the idea of short-range action - the idea of transmitting interactions through the material environment, through the field.

Work on moving a charge in an electric field. Potential difference.

A physical quantity equal to the ratio of the potential energy of an electric charge in an electrostatic field to the magnitude of this charge is called potential

When a test charge q moves in an electric field, the electric forces perform work . This work for small displacement is equal to

Electric field strength as a potential gradient. Equipotential surfaces.

Potential gradient equal to the potential increment per unit length and taken in the direction in which this increment has the greatest value.

Equipotential surface is the surface on which the scalar potential of a given potential field takes on a constant value. Another, equivalent, definition is a surface that is orthogonal to the field lines at any point.

Dipole in an electric field. Electric dipole moment.

uniform field

The total torque will be equal to

inhomogeneous external field

and here a torque arises, turning the dipole along the field (Fig. 4). But in this case, the charges are acted upon by forces of unequal magnitude, the resultant of which is non-zero. Therefore, the dipole will also move translationally, being drawn into the region of a stronger field

Electric dipole moment

Types of dielectrics. Polarization of dielectrics.

Non-polar dielectric- a substance containing molecules with predominantly covalent bonds.

Polar dielectric- a substance containing dipole molecules or groups, or having ions in its structure.

Ferroelectric- a substance containing regions with spontaneous polarization.

Polarization of dielectrics - displacement of positive and negative electrical charges in dielectrics in opposite directions.

Electric field in a dielectric. Polarization vector. Field equation in a dielectric.

In the dielectric the presence electric field does not interfere with the balance of charges. The force acting on the charges in the dielectric from the electric field is balanced by intramolecular forces that hold the charges within the dielectric molecule, so that charge equilibrium is possible in the dielectric, despite the presence of an electric field.

Electric polarization vector is the dipole moment per unit volume of the dielectric.

Field equation in a dielectric

where r is the density of all electric charges

Dielectric susceptibility of a substance. Its relationship with the dielectric constant of the medium.

Dielectric susceptibility of a substance - a physical quantity, a measure of the ability of a substance to polarize under the influence of an electric field. Dielectric susceptibility χe is the linear coupling coefficient between the polarization of the dielectric P and the external electric field E in sufficiently small fields: In the SI system: where ε0 is the electric constant; the product ε0χe is called the absolute dielectric susceptibility in the SI system.

Ferroelectrics. Their features. Piezo effect.

Ferroelectrics, crystalline dielectrics that have spontaneous (spontaneous) polarization in a certain temperature range, which changes significantly under the influence of external influences.

Piezoelectric effect - the effect of dielectric polarization under the influence of mechanical stress

Conductors in an electric field. Distribution of charges in a conductor.

Ε = Evn. - Evn. = 0

Let's introduce a conductor plate into an electric field, let's call this field external .

As a result, the left surface will have a negative charge, and the right surface will have a positive charge. Between these charges, an electric field of its own will arise, which we will call internal. Inside the plate there will simultaneously be two electric fields - external and internal, opposite in direction.

Electrical capacity of conductors. Capacitor. Connection of capacitors.

Electrical capacity - a physical quantity numerically equal to the amount of charge that must be imparted to a given conductor to increase its potential by one.

Capacitor - a device for accumulating charge and energy of an electric field.

parallel connected

series connected

Energy of a charged conductor, capacitor. Electric field energy. Volumetric energy density of the electric field.

Energy of a charged conductor equal to the work that must be done to charge this conductor:

Energy of a charged capacitor

Electrostatic field energy

Volumetric energy density of the electrostatic field

16. Electric field strength and density. EMF. Voltage.

Current strength - a scalar physical quantity determined by the ratio of the charge Δq passing through the cross section of the conductor during a certain period of time Δt to this period of time.

Current density j is a vector physical quantity, the modulus of which is determined by the ratio of the current I in the conductor to the cross-sectional area S of the conductor.

Electromotive force (EMF) - a physical quantity characterizing the work of third-party (non-potential) forces in direct or alternating current sources. In a closed conducting circuit, the EMF is equal to the work of these forces to move a single positive charge along the circuit.

Electrical voltage - a physical quantity whose value is equal to the ratio of the work of the electric field performed when transferring a test electric charge from point A to point B to the value of the test charge.

17. Ohm's law for a homogeneous section of a chain. Ohm's law for an inhomogeneous area in integral form. Ohm's law for a complete circuit.

current strength I in a homogeneous metal conductor is directly proportional to the voltage U at the ends of this conductor and inversely proportional to the resistance R of this conductor

Ohm's law for an inhomogeneous section of a circuit in integral form IR = (φ1 - φ2) + E12

Ohm's law for a complete circuit :

18. Differential form of Ohm's law.

j-current density, σ - specific electrical conductivity of the substance from which the conductor is made Est-field of external forces

19. Joule-Lenz law in integral and differential forms.

in differential form:

thermal power density -

in integral form:

20. Nonlinear elements. Calculation methods with nonlinear elements. Kirchhoff's rule.

nonlinear are called electrical circuits in which reactions and effects are related nonlinearly.

Simple iteration method

1. The original nonlinear equation of the electrical circuit, where is the desired variable, is presented in the form .

2. Calculation is carried out according to the algorithm Where

Iteration step. Linear dependencies

Here is the specified error

Kirchhoff's first rule:

the algebraic sum of current strengths converging at a node is equal to zero

Kirchhoff's second rule:

in any simple closed circuit, arbitrarily chosen in a branched electrical circuit, the algebraic sum of the products of current strengths and the resistances of the corresponding sections is equal to the algebraic sum of the emfs present in the circuit

21. Current in a vacuum. Emission phenomena and their technical applications.

Vacuum is a state of gas in a vessel in which molecules fly from one wall of the vessel to another without ever colliding with each other.

A vacuum insulator, a current in it can only arise due to the artificial introduction of charged particles; for this purpose, the emission (emission) of electrons by substances is used. Thermionic emission occurs in vacuum tubes with heated cathodes, and photoelectron emission occurs in a photodiode.

Thermionic emission is the emission of electrons by heated metals. The concentration of free electrons in metals is quite high, therefore, even at average temperatures, due to the distribution of electron velocities (energies), some electrons have sufficient energy to overcome the potential barrier at the metal boundary. With increasing temperature, the number of electrons, the kinetic energy of thermal motion of which is greater than the work function, increases, and the phenomenon of thermionic emission becomes noticeable.

The phenomenon of thermionic emission is used in devices in which it is necessary to obtain a flow of electrons in a vacuum, for example in vacuum tubes, X-ray tubes, electron microscopes, etc. Electron tubes are widely used in electrical and radio engineering, automation and telemechanics for rectifying alternating currents, amplification electrical signals and alternating currents, generating electromagnetic oscillations, etc. Depending on the purpose, additional control electrodes are used in the lamps.

Photoelectron emission is the emission of electrons from a metal under the influence of light, as well as short-wave electromagnetic radiation (for example, X-rays). The main principles of this phenomenon will be discussed when considering the photoelectric effect.

Secondary electron emission - is the emission of electrons from the surface of metals, semiconductors or dielectrics when bombarded with a beam of electrons. The secondary electron flow consists of electrons reflected by the surface (elastically and inelastically reflected electrons), and “true” secondary electrons - electrons knocked out of the metal, semiconductor or dielectric by primary electrons.

The phenomenon of secondary electron emission is used in photomultiplier tubes.

Vehicle emission is the emission of electrons from the surface of metals under the influence of a strong external electric field. These phenomena can be observed in the evacuated tube.

22. Current in gases. Independent and non-independent conductivity of gases. CVC of current in gases. Types of discharges and their technical applications.

Under normal conditions, gases are dielectrics, because consist of neutral atoms and molecules, and they do not have a sufficient number of free charges. To make a gas conductive, you need to introduce or create free charge carriers - charged particles - into it in one way or another. In this case, two cases are possible: either these charged particles are created by the action of some external factor or introduced into the gas from the outside, or they are created in the gas by the action of the electric field itself existing between the electrodes. In the first case, the conductivity of the gas is called non-independent, in the second - independent.

Current-voltage characteristic (volt-ampere characteristic ) - a graph of the dependence of the current through a two-terminal network on the voltage on this two-terminal network. The current-voltage characteristic describes the behavior of a two-terminal circuit at direct current.

Glow discharge observed at low gas pressures. Used for cathode sputtering of metals.

Spark discharge often observed in nature is lightning. The operating principle of a spark voltmeter is a device for measuring very high voltages.

Arc discharge can be observed under the following conditions: if, after igniting the spark discharge, the resistance of the circuit is gradually reduced, then the current strength in the spark will increase. The electric arc is a powerful light source and is widely used in projection, floodlight and other lighting installations. Due to its high temperature, the arc is widely used for welding and cutting metals. High arc temperatures are also used in the construction of electric arc furnaces, which play an important role in modern electrometallurgy.

Corona discharge observed at relatively high gas pressures (for example, at atmospheric pressure) in a sharply inhomogeneous electric field. It is used in technology for the installation of electric precipitators designed to purify industrial gases from solid and liquid impurities.

23. Magnetic field. Magnetic induction. Magnetic interaction of currents.

A magnetic field - a force field acting on moving electric charges and on bodies with a magnetic moment, regardless of the state of their motion, the magnetic component of the electromagnetic field.

Magnetic induction - a vector quantity that is a force characteristic of the magnetic field (its action on charged particles) at a given point in space. Determines the force with which the magnetic field acts on a charge moving at speed .

Interaction of currents is caused by their magnetic fields: the magnetic field of one current acts as an Ampere force on another current and vice versa.

24. Magnetic moment of circular current. Ampere's law.

Magnetic moment of circular current the strength of the current I flowing along the coil, the area S flowed around by the current and the orientation of the coil in space, determined by the direction of the unit vector normal to the plane of the coil.

Ampere's law the law of mechanical (ponderomotive) interaction of two currents flowing in small sections of conductors located at some distance from each other.

25. Biot-Savart-Laplace law and its application to the calculation of certain magnetic fields:

A) magnetic field of a straight conductor carrying current.

B) the circular current field at the center of the circular current.

Biot-Savart-Laplace law for a conductor with current I, the element dl of which creates the field induction dB at some point A, is written in the form where dl is a vector equal in modulus to the length dl of the conductor element and coinciding in direction with the current, r is the radius vector passed from the conductor element dl to point A of the field, r is the modulus of the radius vector r.

magnetic induction of forward current field

magnetic field induction in the center of a circular conductor carrying current

26. Circulation of magnetic induction. Eddy character of magnetic current. The law of total current in vacuum (the theorem on the circulation of the induction vector).

Magnetic induction circulation where dl is the vector of the elementary length of the contour, which is directed along the circuit bypass, Bl=Bcosα is the component of vector B in the tangent direction to the contour (taking into account the choice of the direction of the circuit bypass), α is the angle between vectors B and dl.

Vortex nature of the magnetic field.

Magnetic induction lines are continuous: they have neither beginning nor end. This occurs for any magnetic field caused by any current-carrying circuits. Vector fields with continuous lines are called vortex fields. We see that the magnetic field is a vortex field. This is the significant difference between a magnetic field and an electrostatic one.

The law of total current for a magnetic field in vacuum (the theorem on the circulation of vector B): the circulation of vector B along an arbitrary closed circuit is equal to the product of the magnetic constant μ0 by the algebraic sum of the currents covered by this circuit:

27. Application of the total current law to calculate the magnetic field of a solenoid.

Ring magnetic circuit

1 and coincide, therefore α = 0;

2 the value of Hx is the same at all points of the contour;

3, the sum of the currents passing through the circuit is equal to IW.

[A/m],

where Lx is the length of the contour along which the integration was carried out;

rx – radius of the circle.

The vector inside the ring depends on the distance rх. If α is the width of the ring

Hav = IW / L,

where L is the length of the average magnetic line.

28. Magnetic flux. Gauss's theorem for the flux of the magnetic induction vector.

Magnetic flux - flux as an integral of the magnetic induction vector through a finite surface. Determined through the surface integral

In accordance with Gauss's theorem for magnetic induction, the flux of the magnetic induction vector through any closed surface is zero:

29. Work on moving a conductor and a circuit with current in a magnetic field.

work on moving a closed loop with current in a magnetic field is equal to the product of the current in the circuit and the change in the magnetic flux coupled to the circuit.

30. Lorentz force. Movement of charged particles in a magnetic field. Accelerators of charged particles in a magnetic field.

Lorentz force - the force with which the electromagnetic field acts on a point charged particle. v-velocity of the particle

. Movement of charged particles in a magnetic field

The basis of the accelerator's operation involves the interaction of charged particles with electric and magnetic fields. An electric field can directly do work on a particle, that is, increase its energy. The magnetic field, creating the Lorentz force, only deflects the particle without changing its energy, and sets the orbit along which the particles move.

31. The phenomenon of electromagnetic induction. Faraday's law. Lenz's rule.

Electromagnetic induction - the phenomenon of the occurrence of electric current in a closed circuit when the magnetic flux passing through it changes.

Faraday's law

Lenz's rule , a rule for determining the direction of the induction current: The induction current arising from the relative movement of the conductive circuit and the source of the magnetic field always has such a direction that its own magnetic flux compensates for changes in the external magnetic flux that caused this current.

32. Induction emf. Law of electromagnetic induction.

Electromotive force (EMF) is a physical quantity that characterizes the work of third-party (non-potential) forces in direct or alternating current sources. In a closed conducting circuit, the EMF is equal to the work of these forces to move a single positive charge along the circuit.

EMF can be expressed in terms of the electric field strength of external forces (Eex). In a closed loop (L) then the EMF will be equal to: , where dl is the contour length element.

Law of Electromagnetic Induction Email current in a circuit is possible if external forces act on the free charges of the conductor. The work done by these forces to move a single positive charge along a closed loop is called emf. When the magnetic flux changes through the surface limited by the contour, extraneous forces appear in the circuit, the action of which is characterized by the induced emf.

33. Self-induction. Inductance.

Self-induction - excitation of the electromotive force of induction (emf) in an electrical circuit when the electric current in this circuit changes; a special case of electromagnetic induction. The electromotive force of self-induction is directly proportional to the rate of change of current

Inductance (from Latin inductio - guidance, motivation), a physical quantity characterizing the magnetic properties of an electrical circuit. The current flowing in a conducting circuit creates a magnetic field in the surrounding space, and the magnetic flux Ф penetrating the circuit (linked to it) is directly proportional to the current strength I:

34. The phenomenon of mutual induction. Mutual induction coefficient.

The phenomenon of mutual induction called the induction of EMF in one circuit when the current changes in another.

Ф21 = M21I1 Coefficient M21 is called mutual inductance the second circuit depending on the first.

35. Magnetic field energy. Magnetic field energy density.

Magnetic field energy

Magnetic field energy density (H-magnetic field strength).

36. Magnetic properties of matter. Magnetization of matter. Gauss's theorem for magnetic field induction.

By magnetic properties all substances can be divided into three classes:

substances with pronounced magnetic properties - ferromagnetic; their magnetic field is noticeable at considerable distances

paramagnetic; their magnetic properties are generally similar to those of ferromagnetic materials, but much weaker

diamagnetic substances - they are repelled by an electromagnet, i.e. the force acting on diamagnetic materials is directed opposite to that acting on ferro- and paramagnetic materials.

magnetization of matter

Gauss's theorem for magnetic induction

The flux of the magnetic induction vector through any closed surface is zero:

or in differential form:

This is equivalent to the fact that in nature there are no “magnetic charges” (monopoles) that would create a magnetic field, just as electric charges create an electric field. In other words, Gauss's theorem for magnetic induction shows that the magnetic field is (fully) vortex.

37. Magnetic field strength. Theorem on the circulation of the magnetic field strength vector.

Magnetic field strength - (standard designation H) is a vector physical quantity equal to the difference between the magnetic induction vector B and the magnetization vector M.

, where μ0 is the magnetic constant

Theorem on the circulation of the magnetic field strength vector:

The circulation of the magnetic field of direct currents along any closed circuit is proportional to the sum of the current strengths penetrating the circulation circuit.

38. The law of total current in matter.

total current law : The circulation of the magnetic field strength vector along any closed circuit L is equal to the algebraic sum of the macrocurrents covered by the circuit.

39. Magnetic susceptibility and magnetic permeability of matter.

Magnetic permeability is a physical quantity that characterizes the relationship between magnetic induction B and magnetic field strength H in a substance.

40. Dia-, para- and ferromagnets.

CM. №36

41. Electromagnetic oscillations in an oscillatory circuit. Thomson's formula.

The resonant frequency of the circuit is determined by the so-called Thomson formula

Thomson's formula

42. Maxwell's equation in integral form.

Using the Ostrogradsky-Gauss and Stokes formulas, Maxwell's differential equations can be given the form of integral equations:

Gauss's law

Gauss's law for magnetic field

Faraday's Law of Induction

Work function

the energy expended to remove an electron from a solid or liquid into a vacuum. The transition of an electron from a vacuum to a condensed medium is accompanied by the release of energy equal to R.v. Consequently, R. v. is a measure of the connection of an electron with a condensed medium; The smaller the RV, the easier the emission of electrons occurs. Therefore, for example, the current density of thermionic emission (see Thermionic emission) or field emission (see Tunnel emission) depends exponentially on R.V.

R.v. most fully studied for conductors, especially for metals (See Metals). It depends on the crystallographic structure of the surface. The more densely the crystal face is “packed,” the higher the R.V. φ. For example, for pure tungsten φ = 4.3 ev for edges (116) and 5.35 ev for faces (110). For metals, an increase (averaged over faces) φ approximately corresponds to an increase in ionization potential. Smallest R.v. (2 ev) are characteristic of alkali metals (Cs, Rb, K), and the largest (5.5 ev) - metals of the Pt group.

R.v. sensitive to surface structure defects. The presence of its own disordered atoms on a close-packed face reduces φ. φ depends even more sharply on surface impurities: electronegative impurities (oxygen, halogens, metals with φ , greater than the φ of the substrate) usually increase φ, and electropositive ones - decrease. For most electropositive impurities (Cs on W, Tn on W, Ba on W), a decrease in RV is observed, which reaches at a certain optimal impurity concentration n opt minimum value lower than φ of the base metal; at n≈ 2n wholesale R.v. becomes close to φ of the coating metal and does not change further (see. rice. ). Size n opt corresponds to an ordered layer of impurity atoms consistent with the structure of the substrate, as a rule, with all vacant places filled; and magnitude 2 n opt - dense monoatomic layer (coordination with the structure of the substrate is broken). T. o., R. v. at least for materials with metallic electrical conductivity is determined by the properties of their surface.

The electronic theory of metals considers R. v. as the work required to remove an electron from the Fermi level into vacuum. Modern theory does not yet allow us to accurately calculate φ for given structures and surfaces. Basic information about the values of φ is provided by experiment. To determine φ, emission or contact phenomena are used (see Contact potential difference).

Knowledge of R.v. essential in the design of electrovacuum devices (See Electrovacuum devices), where the emission of electrons or ions is used, as well as in devices such as thermionic energy converters (See Thermionic converter).

Lit.: Dobretsov L.N., Gomoyunova M.V., Emission Electronics, M., 1966; Zandberg E. Ya., Ionov N. I., Surface ionization, M., 1969.

V. N. Shrednik.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what “Work Work” is in other dictionaries:

The difference between the minimum energy (usually measured in electron volts) that must be imparted to an electron for its “direct” removal from the volume of a solid, and the Fermi energy. Here “immediacy” means that the electron... ... Wikipedia

Energy F must be expended to remove electron from a solid or liquid into a vacuum (into a state with zero kinetic energy). R.v. Ф=еj, where j is the potential of the R.V., e abs. electrical value electron charge. R.v. equal to the difference... ... Physical encyclopedia

work function- electron; work function Work corresponding to the energy difference between the level of chemical potential in the body and the potential level near the surface of the body outside it in the absence of an electric field... Polytechnic terminological explanatory dictionary

The work required to remove an electron from a condensed substance into a vacuum. It is measured by the difference between the minimum energy of an electron in a vacuum and the Fermi energy of electrons inside the body. Depends on the condition of the surface... ... Big Encyclopedic Dictionary

WORK WORK, the energy expended to remove an electron from a substance. Taken into account in the PHOTOELECTRIC EFFECT and in THERMOELECTRONICS... Scientific and technical encyclopedic dictionary

work function- The energy required to transport to infinity an electron located in its original position at the Fermi level in a given material. [GOST 13820 77] Topics: electrovacuum devices... Technical Translator's Guide

work function- the energy expended to remove an electron from a solid or liquid into a vacuum. The transition of an electron from a vacuum to a condensed medium is accompanied by the release of energy equal to the work function; the lower the work function, the... ... Encyclopedic Dictionary of Metallurgy

work function- Work Function The minimum energy (usually measured in electron volts) that must be expended to remove an electron from the volume of a solid. An electron is removed from a solid through a given surface and moves to... Explanatory English-Russian dictionary on nanotechnology. - M.

The work required to remove an electron from a condensed substance into a vacuum. It is measured by the difference between the minimum energy of an electron in vacuum and the Fermi energy of electrons inside the body. Depends on the condition of the surface... ... encyclopedic Dictionary

work function- išlaisvinimo darbas statusas T sritis Standartizacija ir metrologija apibrėžtis Darbas, kurį atlieka 1 molis dalelių (atomų, molekulių, elektronų) pereidamas iš vienos fazės į kitą arba į vakuumą. atitikmenys: engl. work function vok.… … Penkiakalbis aiškinamasis metrologijos terminų žodynas

work function- išlaisvinimo darbas statusas T sritis fizika atitikmenys: engl. work function; work of emission; work of exit vok. Ablösearbeit, f; Auslösearbeit, f; Austrittsarbeit, f rus. work function, f pranc. travail de sortie, m … Fizikos terminų žodynas

Let's consider the situation: charge q 0 enters an electrostatic field. This electrostatic field is also created by some charged body or system of bodies, but we are not interested in this. A force acts on the charge q 0 from the field, which can do work and move this charge in the field.

The work of the electrostatic field does not depend on the trajectory. The work done by the field when a charge moves along a closed path is zero. For this reason, electrostatic field forces are called conservative, and the field itself is called potential.

Potential

The "charge - electrostatic field" or "charge - charge" system has potential energy, just as the "gravitational field - body" system has potential energy.

A physical scalar quantity characterizing the energy state of the field is called potential a given point in the field. A charge q is placed in a field, it has potential energy W. Potential is a characteristic of an electrostatic field.

Let's remember potential energy in mechanics. Potential energy is zero when the body is on the ground. And when a body is raised to a certain height, it is said that the body has potential energy.

Regarding potential energy in electricity, there is no zero level of potential energy. It is chosen randomly. Therefore, potential is a relative physical quantity.

In mechanics, bodies tend to occupy a position with the least potential energy. In electricity, under the influence of field forces, a positively charged body tends to move from a point with a higher potential to a point with a lower potential, and a negatively charged body, vice versa.

Potential field energy is the work done by the electrostatic force when moving a charge from a given point in the field to a point with zero potential.

Let us consider the special case when an electrostatic field is created by an electric charge Q. To study the potential of such a field, there is no need to introduce a charge q into it. You can calculate the potential of any point in such a field located at a distance r from the charge Q.

The dielectric constant of the medium has a known value (tabular) and characterizes the medium in which the field exists. For air it is equal to unity.

Potential difference

The work done by a field to move a charge from one point to another is called potential difference

This formula can be presented in another form

Equipotential surface (line)- surface of equal potential. The work done to move a charge along an equipotential surface is zero.

Voltage

The potential difference is also called electrical voltage provided that external forces do not act or their effect can be neglected.

The voltage between two points in a uniform electric field located along the same line of intensity is equal to the product of the modulus of the field strength vector and the distance between these points.

The current in the circuit and the energy of the charged particle depend on the voltage.

Superposition principle

The potential of a field created by several charges is equal to the algebraic (taking into account the sign of the potential) sum of the potentials of the fields of each field separately

When solving problems, a lot of confusion arises when determining the sign of potential, potential difference, and work.

The figure shows tension lines. At which point in the field is the potential greater?

The correct answer is point 1. Let us remember that the tension lines begin on a positive charge, which means the positive charge is on the left, therefore the leftmost point has the maximum potential.

If a field is being studied that is created by a negative charge, then the field potential near the charge has a negative value; this can be easily verified if a charge with a minus sign is substituted into the formula. The further away from the negative charge, the greater the field potential.

If a positive charge moves along the tension lines, then the potential difference and work are positive. If a negative charge moves along the tension lines, then the potential difference has a “+” sign, and the work has a “-” sign.