Differential form of the law of Oma. Find the connection between current density j. and field strength E. In the same point of the conductor. In an isotropic conductor, an ordered movement of current carriers occurs in the direction of the vector E.. Therefore, vectors direction j. and E. match up. Consider in a homogeneous isotropic environment Elementary volume with forming, parallel vector E., Length bounded by two equipotential sections 1 and 2 (Fig. 4.3).
Denote by their potentials and, and the average cross-sectional area through. Using Ohm's Law, we get for current, or for current density, therefore
We turn to the limit at, then the volume under consideration can be considered cylindrical, and the field inside it is homogeneous, so
where E. - Tension electric field inside the conductor. Considering that J. and E.coincide in the direction we get
.
This ratio is differential form of the law Ohm for a homogeneous section of the chain. The value is called specific conductivity. In an inhomogeneous section of the chain on current carriers, there are other electrostatic forces, and third-party strengths, therefore, the current density in these areas is proportional to the sum of tensions. Accounting for this leads to differential form Ohm law for heterogeneous regimen chain.
.
When passing electric current In the closed chain on free charges, the forces on the part of the stationary electric field and third-party power are acting. At the same time, in some sections of this circuit, the current is created only by a stationary electric field. Such sections of the chain are called uniform. In some areas of this chain, in addition to the power of a stationary electric field, third-party forces act. The plot of a chain on which third-party power is called, called inhomogeneous plot of chain.
In order to find out what the current is depends on these sites, it is necessary to clarify the concept of voltage.
Consider at first a homogeneous section of the chain (Fig. 1, a). In this case, the work on the movement of charge makes only the forces of the stationary electric field, and this area characterize the difference in potentials Δ φ . The difference of potentials at the ends of the section Δ φ =φ 1−φ 2=AKQ.where A. K - work of the power of a stationary electric field. The inhomogeneous section of the chain (Fig. 1, b) contains, unlike a homogeneous site, the source of EDC, and to work forces electrostatic field On this site, the work of third-party forces is added. A-priory, Aelq.=φ 1−φ 2, where q. - a positive charge that moves between any two chain points; φ 1−φ 2 - the difference in potentials of points at the beginning and end of the section under consideration; ASTQ.=ε . Then they talk about tension for tension: E. Stats. e. p. \u003d. E. E / Stat. p. +. E. Stor. Voltage U. on the plot of chains is a physical scalar valueequal to the total work of third-party strength and forces of the electrostatic field to move a single positive charge on this site:
U.=AKQ.+AstorQ.=φ 1−φ 2+ε .
From this formula, it can be seen that in general, the voltage in this section of the chain is equal to the algebraic amount of the potential difference and the EMF in this area. If only on the site is valid electric power (ε \u003d 0) then U.=φ 1−φ 2. Thus, only for a homogeneous section of the chain of the concept of voltage and the difference in potentials coincide.
Ohm law for not uniform plot Chains looks like:
I.=Ur.=φ 1−φ 2+εr.,
where R. - the overall resistance of the inhomogeneous site.
EMF. ε It can be both positive and negative. This is due to the polarity of the inclusion of EMF in the area: if the direction generated by the current source coincides with the direction of the current passing in the site (the current direction on the site coincides inside the source with the direction from the negative pole to the positive), i.e. EMF contributes to the movement of positive charges in this direction, ε \u003e 0, otherwise, if the EMF prevents the movement positive charges in this direction, then ε < 0.
Calculation of electrical chains direct current Based on the use of the Ohm law. For a homogeneous section of the chain of the application of the Ohm law, were considered in detail in the previous paragraph. How to find current strength in an inhomogeneous site electrical chainAt the ends of which there is some potential difference and inside which there are horse racing, for example, a galvanic element or battery is included?
Contact difference potentials. We first consider the inhomogeneous section of the chain consisting of two successively connected different conductors A and B, for example, copper and zinc (Fig. 73). Experience shows that there is a potential jump between different conductors, which does not depend on the current and exists even in its absence. This contact potential difference was opened in 1797 by the Italian physicist A. Volta, who established a number of metals in which each previous metal, when connected to any of the following, is connected positively: AL, ZN, SN, CD, PB, SB, BI, HG , FE, CU, AG, AU, PT, PD.
Fig. 73. Inhomogeneous section of the chain
The existence of a contact potential difference can be demonstrated using the following simple experience. On the terminal of the electroscope, the plate is strengthened from the test metal (Fig. 74).
Fig. 74. Detection of contact potential difference
It is covered with a thin layer of insulating material. The plate is placed from the second test material, equipped with an insulating handle, and combine this plate with the ground.
Plates for a while connect the conductor. At the same time, the contact difference of potentials arises between the plates, i.e. the condenser formed by them is charging. However, the voltage existing in it is so small in it that it is impossible to detect the deviation of the leaflets of the electroscope. Therefore, they are applied as follows. The upper plate is raised, so the capacitance of the condenser formed by the plates decreases. Since the charge on an isolated lower plate remains unchanged, the potential difference between it and the ground increases at as many times as the container decreases. With sufficient sliding plates, the deviation of the leaflets of the electroscope is easily detected.
The physical reason for the occurrence of the contact difference of potentials is the difference in the operation of the exit from different metals, i.e., the minimum work that needs to be made to remove the electron electron into the vacuum, as well as in the difference in the concentration of free electrons in them. The magnitude of the race of the potential depends on the kind of metals, the purity of their surfaces and on their temperature. The contact difference of potentials ranges from several tenths of Volta to Units Volt.
If you combine sequentially somewhat different metals, then the difference in potentials arising at the ends of the extreme conductors does not depend on which conductors are between them, i.e. it will be the same as with the direct connection of these extreme conductors among themselves. We emphasize that in the absence of current, each metal remains equipotential, and the height of the potential and the associated electric field There are only at the point of contact.
Current in an inhomogeneous section of the chain. Connect now the external ends of the conductors A and B in fig. 73 to the source of constant voltage. Denote the potential of the left end of the conductor, but through and the potential of the right end of the conductor in through the potentials of metals A and in the contact site we denote through as now in the conductors there is a current, then, of course, we don't know how to record the law of Oma for the entire area of \u200b\u200bthe chain But we can write it back for each of the homogeneous sites A and B. Since the conductors are connected in series, then through them the same current is supposed to assume that the current goes from left to right, as shown in Fig. 73. Thuschy
where - the resistance of the plots A and V. Moving the metering equation (1) and regroup the components in the left side as follows:
The amount is the full resistance of the site under consideration. The potential difference is an applied voltage. The difference is a potential jump in the place of contact of metals, which, as already noted, does not depend on the flowing current and is determined only by the nature of metals and temperature. The value of the jump will be denoted through the skin \u003d 2) can be rewritten as
This is the law of Oma for the inhomogeneous section of the chain.
It should be noted that a difference is understood under the stress in the section under consideration - where - the potential of the point from which the current flows, and the potential of the point to which the current flows. The potential jump in the contact site is defined as, i.e. the sign is determined by it increases or lowers the jump the value of the potential in the circuit in the current direction: if it increases, if lowers,
But after reasoning, we chose the direction of the current from left to right at random! And if in reality it flows in the opposite direction? Suppose that the current flows on the right left, and repeating literally all the calculations, we will get the value of the current strength, differing only in the sign. This means that, starting to analyze the inhomogeneous section of the chain, we can not think about how the current actually flows, but to ask him arbitrarily.
By selecting the current direction, we determine its value according to formula (3), strictly observing the above-mentioned rule of signs for if the current turns out to be positive, then it really flows in the direction specified by us. If a negative value is negative, then actually flows in the opposite direction, and the value of it, of course, is found correctly. Below, we will consider in detail examples of using the Ohm law for an inhomogeneous section of the chain, illustrating the formulated rule of signs.
If you connect sequentially several different conductors, then, repeating all the above calculations, it is easy to ensure that the formula (3) retains its kind; Only now it is necessary to understand the algebraic amount of potential surges in contacts, and under the amount of the resistance of all conductors.
Closed inhomogeneous chain. Consider now a closed chain of conductors, composed of different metals. Imagine that this closed chain is obtained as a result of the initiation of the beginning and end of the chain of the conductors, i.e., those points to which
there could be an external voltage to compound these points into one means that now the formula (3) for a closed sequential chain takes the view
where - the algebraic amount of the potential jumps between all pairs of the connected conductors, the impedance of the closed chain.
If the contacts between different metals are at the same temperature, the sum of all potential jumps will be obviously zero, since the potential jump between any two metals does not depend on what is between them.
Electromotive force. With different contact temperatures in the chain, the amount of potential jumps can be different from zero, and the circuit will go the current defined by formula (4). The amount of potential jumps in a closed chain is called electromotive power (EMF), and equality (4) - Ohm's law for a closed unbranched chain.
Let us dwell on the physical sense of the concept of EDC. The potential jump at the point of contact of two metals occurs due to the difference in the operation of the electron output and their concentration in these metals, leading to diffusion of electrons through contact. Forces causing the directional flow of electrons have non-electrostatic (non-Coulomb) origin. Such forces of non-electrostatic origin, regardless of their physical nature, are called third parties. The directional flow of electrons through contact is terminated when an electrostatic field prevents it, which balancing the effect of third-party forces. This is an emerging electrostatic field and is characterized by a contact difference of potentials.
In the case considered case, the electromotive force occurs only at different contact temperatures and is called thermoelectro-moving force (thermo-emotes).
Ohm (4) law for a closed chain is fair not only for thermopower, but also for third-party forces of any nature. As already noted, the inhomogeneity of the chain may be due to the inclusion of a galvanic element, a battery, a DC generator, etc. If the circuit under consideration contains several EDFs, then in formula (4) it is necessary to understand the algebraic amount of all these EDS, and each Of these, it is determined in accordance with the rule formulated above.
Below will be shown that EMF characterizes the work of third-party forces committed when moving charges. In other words, EMF characterizes the conversion of other types of energy into electric.
EMF in different sources. In contrast to the contacts of the first-type conductors (metals, semiconductors), in which no chemical changes occur during the passage of electric current, in the contacts of metals with electrolytes (for example, zinc with sulfuric acid) occur chemical reactions. As we saw, in a closed chain from various conductors of the first kind, with the same temperature, it does not occur in the same temperature. If you make a closed chain from the conductors of the first and second kind, then it occurs different from zero EMF even at a constant temperature.
Fig. 75. Daniel element and appearance Dry element of lawshest
Such a combination of conductors of the first kind and electrolytes is a chemical current source "dry" galvanic element, or battery (Fig. 75), in which the electric current is maintained due to chemical reactions between the electrodes and the electrolyte. For example, in a galvanic element consisting of zinc and copper plates immersed in a sulfuric acid solution, a zinc electrode is dissolved in acid. In batteries, reversible chemical reactions are used: the electrode is spent during operation during the charging process. Chemical sources of current provide EMF to 2 V.
In the generators used on power plants to transform mechanical energy into electrical, third-party forces by nature are the forces acting on the charges moving in the magnetic field.
Internal resistance of the current source. In any real electrical circuit, you can always select a plot that serves to maintain the current (current source), and the rest is considered as a "load". In the source of the current, third-party strengths necessarily act, therefore, in general, it is characterized by an electromotive force and resistance that is called the internal resistance of the source. The load also may contain an emf (for example, an electric motor), however, in the simplest case, no third-party forces act in the load, and it is characterized only by resistance.
The simplest closed chain. Consider a closed electrical circuit containing a current source with EMF and internal resistance and a load characterized by resistance only
(Fig. 76). The resistance of the connecting wires will be considered equal to zero. Applying to such a circuit formula (4), in the denominator which is a complete resistance of the chain, write it in the form
where through marked load resistance. The ideal voltmeter connected to the resistance i.e. to the clamping (poles) of the operating current source, shows the voltage as follows from the Ohm law for a homogeneous section of the chain - in this case for the load resistance. Substituting current current from (5), this voltage can be expressed through the parameters of the chain
Fig. 76. Simplest closed chain with current source
From (6) it can be seen that the voltage at the clamping source is always less than its EDC. It is the closer to the more load resistance. In the limit (more precisely, when that is, when you can neglect the resistance of the source compared to the load resistance) from (6) it follows that the voltage on the clips of the open source is equal to its EMF.
The opposite grade (more precisely, when that is, when the load resistance is much less internal) corresponds to the so-called short circuit of the current source. In this case, a
Current short circuit, i.e. the maximum current that can be obtained from this source.
From formula (5) it follows that the voltage on the source clips can be written as
The product is the voltage at the resistance i.e. voltage inside the current source. Therefore, formula (8) means that the EMF is equal to the amount of stresses at the external and inner sections of the closed chain.
Composite external chain. As a rule, the outer chain consists of several resistance, differently interconnected. All of the above remains fair, if under understand the equivalent resistance of the entire external chain. The reduced ratios make it easy to calculate such chains or to conduct their qualitative analysis.
Consider the following examples.
1. It is required to determine how the readings of all the ideal voltmeters in the circuit shown in Figure will be determined. 77, if, for example, reduce the resistance of an alternating resistor.
When decreasing the power of the current in the chain increases. In accordance with the Ohm's law, the voltage on the resistance voltage increases, and the voltage at the clips of the current source, as follows from formula (8), decreases.
Fig. 77. To the study of voltmeter readings
Fig. 78. To the study of changes in ammeter readings
Apply Ohm's law for a plot of chain to resistance is difficult, since decreases, and the current in the chain increases. So we use what it is immediately clear that the voltage on the resistor decreases, and more
1. It is required to determine how the readings of all the ideal ammeters in the diagram shown in Fig. 78, with a decrease in resistance, it is obvious that with a decrease in the total load resistance decreases, and the current I, shown by the ammeter A, increases. At the same time, as follows from (8), the voltage on parallel to the connected resistances and decreases. Therefore, the current shown by the ammeter decreases. To say right away, which will happen with an ammeter reading difficult. However, it immediately follows from equality, which increases, moreover, more than I.
What is the contact difference potential? How can your experience be ensured in its existence?
Show how using the Ohm law for a homogeneous section of the chain, you can obtain formula (3).
Explain the rule of signs that should be guided by the use of formula (3).
What is an electromotive force? Explain physical meaning The concepts of EMF on the example of a chain from different metals. What is third-party strength?
Word Ohma law for a closed unbranched chain.
What reasons are the EMF in the chain from different metals or semiconductors, in chemical sources of current, in electrical generators?
Highlight the main parts of any real closed chain. What parameters are they characterized?
How is the voltage on the source included with its EMF? What does the voltage within the source depend on?
Voltage at the current source. Let's return to formula (8). It was obtained as a consequence of the law of Oma for a closed chain expressed by formula (5).
Fig. 79. The current source as an inhomogeneous section of the chain (B) and the compensatory method of measuring EMF (b)
Let us calculate the current through the source, considering it as an inhomogeneous section of the chain (Fig. 79a). Using formula (3), in accordance with the above signs above, we have
It is easy to see that the voltage appears in the formula (8) is equal to the ratio (9) actually coincides with (8). However, with this output of this formula, the assumption was not used that the current is created only by this source (i.e. that therefore formula (8), as and (9),
in fact, it is valid for any ratio between the potentials characterizing the voltage at the current source.
EMF measurement. The definition of an EDC of a source on experience is usually produced by the so-called compensation method, when an unknown EMF is compared with a well-known EMF of another, reference source. For this, the diagram shown in Fig. 79b. The battery, the EMF of which is obviously greater than the EDC of the reference source 0 and the measured closes to the external resistance. Using the switch to to some part of this resistance, you can connect either a reference source or measured. The polarity of the inclusion of elements is shown in Fig. 79b.
I will first connect the reference source with EMF and select the resistance so that the current through the galvanometer is, and therefore, and through the reference source turned to zero. Reminer value
Explain why the voltage appears in the formula (8) is really equal and not
What are the advantages of the compensatory method of measuring EDC?
In an inhomogeneous section of the chain on the current carriers, there are except electrostatic forces, third-party forces. Third-party forces are able to cause an ordered movement of current carriers to the same extent as the forces are electrostatic. In the previous paragraph, we found out that in a homogeneous conductor, the average rate of ordered movement of current carriers is proportional to electrostatic strength. Obviously, there, where, in addition to electrostatic force, there are third-party forces on carriers, the average rate of ordered movement of carriers will be proportional to the total strength. Accordingly, the current density at these points turns out to be a proportional sum of tensions
Formula (35.1) shall generalize formula (34.3) in case of an inhomogeneous conductor. It expresses in differential uniforms the law of Oma for the inhomogeneous section of the chain.
From the law in differential form, you can go to integral form Ohm's law. Consider an inhomogeneous section of the chain. Suppose that within this area there is a line (we will call it in the current circuit), satisfying the following conditions: 1) in each section perpendicular to the contour, the values \u200b\u200bare with sufficient accuracy; 2) Vectors at each point are aimed at the contour. The cross section of the conductor may be non-permanent (Fig. 35.1).
Choose an arbitrarily direction of the contour. Let the selected direction correspond to the movement from the end 1 to the end of 2 of the section of the chain (direction 1-2). We design vectors included in the ratio (35.1), on the contour element. As a result, we get
By virtue of the assumptions, the projection of each of the vectors is equal to the vector module taken with a plus sign or minus, depending on how the vector is directed relative to. For example, if the current flows in direction 1-2, and if the current flows in the direction 2-1.
Due to the preservation of the charge, the power of direct current in each cross section should be the same. Therefore, the magnitude is constant along the contour. Current strength in this case should be considered as an algebraic value.
Recall that the direction 1-2 we chose arbitrarily. Therefore, if the current flows in the selected direction, it should be considered positive; If the current flows in the opposite direction (i.e. from the end 2 to the end 1), its strength should be considered negative.
Replace in (35.2) by the relationship and the conductivity of specific resistance . As a result, the ratio will turn out
Multiply this ratio on and integrating along the contour:
The expression is the resistance of the length of the length of the length and the integral of this expression is the resistance R section of the chain. The first integral in the right part gives the second integral - valid on the site. So we come to the formula
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Ohm law for an inhomogeneous section of the chain.
To occur in the electrical current conductor, it is necessary that the electrical field existed inside the conductor, the sign of which is the presence of potential difference at the ends of the conductor.
Create an electric field in an electrical circuit can be at the expense of the charges available in it. To do this, it is enough to divide the charges of opposite signs, focusing in one area of \u200b\u200bthe chain an excessive positive charge, in the other - negative (to create noticeable fields, it is enough to share a negligible part of charges).
The separation of multi-dimensional charges cannot be carried out by the power of electrostatic (Coulomb) interaction, since these forces not only do not disconnect, but on the contrary, they seek to connect the charges of opposing signs, which inevitably leads to equalization of potentials and the disappearance of the field in conductors. The separation of multimenamic charges in the electrical circuit can be carried out only by non-electrical origin.
Forces separating charges in the electrical circuit, creating an electrostatic field in it, are called third-party.
Devices in which third-party power are called sources of current.
The nature of third-party strength may be different. In some sources, these forces are due to chemical processes (galvanic elements), in other - diffusion of charge carriers and contact phenomena (contact EDC), in the third - the presence of a vortex electric field (electrical generators), etc. Third-party forces act on charges only in current sources, and there they act either all the ways of following charges through the source or in some sections. In this regard, they talk about sources with distributed and focused third-party forces. An example of a source with distributed third-party forces can be an electrical generator - in it these forces act on the entire length of the anchor winding; An example of a source with focused third-party forces can be a galvanic element - in it these forces act only in the finest layer adjacent to the electrodes.
Since third-party valid only in the source, but electrostatic - and in the source and in the external chain, then there are areas in any chain, where third-party and electrostatic forces are also operating on charges. A plot of chain in which only electrostatic forces act on charges is called, as already mentioned, uniform. The plot in which electrostatic, and third-party power are also operating on charges inhomogeneous. In other words, a non-uniform area is a plot containing the current source.
When moving charges for such a plot, electrostatic and third-party forces make work. Third-party work characterizes electromotive force (Abbreviated EDC).
The electromotive force on this section of the chain 1-2 is called a scalar physical quantity, numerically equal to the work performed by third-party forces when moving a single, positive point charge From point 1 to point 2
The work of electrostatic forces characterizes potential difference.
The potential difference between points 1 and 2 of the electrical circuit is called a scalar physical quantity, numerically equal to the operation performed by electrostatic forces when moving a single, positive point charge from point 1 to point 2
.
The joint work of third-party and electrostatic forces on this section of the chain characterizes the voltage.
The voltage in this section 1-2 is the physical quantity, numerically equal to the algebraic amount of work performed by electrostatic and third-party forces when moving a single, positive point charge from the point1 exactly2 .
.
Or, in other words, 
.
If the resistance of the inhomogeneous site 1-2 Equally, the current flows I. , Taking advantage of the law of conservation of energy, it is possible to obtain the law of Oma for the inhomogeneous section of the chain.
If the current in the chain is stationary, the plot of the chain is still not changed and its temperature does not change, the only result of the current operation on this site will be the highlight of heat to the environment. Complete operation of current, folding from the works of electrostatic and third-party forces, during t. equal to the number of heat excreted.
and 
.
Then, and after cuts
.
From here 
- Ohm law for an inhomogeneous section of the chain in the integral form: the strength of the current in the inhomogeneous section of the electrical value is directly proportional to the algebraic amount of the potential difference at the ends of the section and the EMF, acting in this section, and inversely proportional to the full resistance of the site.
The strength of the current, the difference of potentials and the EMF in this formula is the magnitude of algebraic. Their sign depends on the direction of parting the site. If the direction of the current coincides with the direction of bypass, it is considered positive. If the current source sends a current in the direction of bypass, its EMF is considered positive. The following is an example of the entry of the Ohm law for an inhomogeneous section of the chain shown in Fig. 52.
When bypass from a to 
,
from in to a 
.
That is, when changing the direction of bypass, all the values \u200b\u200bincluded in the Ohm law change the sign.
Thus, the law of Oma and for homogeneous and for inhomogeneous sites is one of the manifestations of the law of conservation and turning the energy.
4.5. The consequences of the Ohm law for the inhomogeneous section of the chain.
Consider the consequences arising from the Ohm law for the inhomogeneous section of the chain.
1. If there is no current source in this section (
12
=0
), then we get the law of Oma for a homogeneous site 
,
from where it follows that 
or 
.
The voltage and the difference of potentials on a homogeneous section of the chain are equal to each other.
2. If you consider a closed chain, then or. Substituting it in the original formula, we get
where
- full chain resistance- resistance to the outer section of the chain, - resistance of the inner portion of the chain (current source).
Then.
The strength of the current in a closed circuit is directly proportional to the EMF and inversely proportional to the full chain resistance- Ohm's law for the full chain.
3. If the circuit is open, there is no current in it ( I.=0 ) IR=0 .
Then 
, i.e EMF is equal in absolute value and is opposite to the sign of the potential difference at the clips of the open source.
4.6. Power in DC circuit.
The power of the electric current on a homogeneous area of \u200b\u200bthe chain with resistance is sufficiently simple can be found as the ratio of the work performed by the electrostatic field to move in charges of charges by the time for which this work is performed:
In this way, the power of the electric current on the circuit section is proportional to the square of the current strength and the resistance of the site.
If you consider a closed chain (Fig. 53), then in such a chain it is customary to consider two types of power - complete and useful. Full Called the power that stands out throughout the circuit, that is, both on the external resistance and on the internal resistance of the current source. Then complete power can be found as a product of the current of the current for the total chain resistance:
, and using the Ohm law for a closed chain, we get:
.
Useful call the power that stands out on the external resistance of the chain, that is, it is equal 
And again applies the Ohm law for a closed chain, we get: 
.
Efficient efficiency (efficiency) a closed chain call the ratio of useful power to full. Using the derived formulas, we get:
We find out how useful, full power and efficiency depend on the resistance of the external chain. It can be seen that the complete power is maximal when and decreases with increasing external resistance. Useful power at first increases from zero to some value, and then decreases with growth. To find out with what value the useful power is maximal, it is necessary to equate to zero derivative.
from here after cutting we get
Thus, the maximum power in the outer chain develops, provided that the resistance of the outer chain is equal to the internal resistance of the current source. We note that with this condition, the efficiency is only 0.5, that is, only half of the power developed by the source of the current is released in the outer chain, the remaining power goes to heating the source itself. 
In fig. 54 graphically depicts the dependences of complete and useful power, as well as the efficiency for a closed chain from the external resistance of the chain.
Bibliographic list
Savelyev I.V. Course of general physics: T.2. Electricity. - M.: Science, 1987. - 432 p.
Trofimova T.I. Course of physics: studies. Handbook for universities. - 7th ed., Ched. - M.: Higher. School, 2003. - 542 C.: IL.
Detlaf F.F., Yavorsky B.M. Course of physics: studies. Handbook for themp. - M.: Science, 1989. - 608 p.
Preface .......................................................................................... 3
1. Electric field in vacuum .................................................................. 4
1.1. Electromagnetic field - material carrier
electromagnetic interaction .................................................... 4
1.2. Electric charges ............................................................... .......
1.3. Cut law ............................................................... ..................... 5
1.5. Principle of superposition of fields ............................................................. 7
1.6. Calculation of electric fields based on the principle of superposition ............... 8
1.7. Lines of tension vector ...................................................... ..10
1.8. Stream vector of tension ...................................................... ... 11
1.9. Gaussian theorem ................................................................................ 13
1.10. The use of the Gauss Theorem to the calculation of electric fields .................12
1.11. Work of the power of the electrostatic field .............................. ..................... 18
1.12. Circulation of the tension of the electrostatic field ......... ...... 19
1.13. The potential of the electrostatic field ................................. ................. 20
1.14. Communication between the tension and the potential of the electrostatic field..21
1.15. Calculation of the potential and potential difference in the electrostatic field ... 23
2. Electric field in dielectrics ................................................................. ... 24
2.1. Conductors, dielectrics, semiconductors .................................... ... 24
2.2. Polarization of dielectrics ............................................................ 25
2.3. Polarization types .......................................................................26
2.4. The relationship of the values \u200b\u200bcharacterizing polarization ............ ................. 28
2.5. Electric field in dielectrics .................................... ................. 29
2.6. Vector of electrical displacement ....................................... ................. 30
2.7. Calculation of the electric field in the presence of dielectrics ........................ 33
2.8. Segnetoelectrics ........................................................................ 33.
2.9. Piezoelectric effect. Electrotrix ................................. ... 35
3. Conductors in the electric field. Electric field energy ................36
3.1. Distribution of charges on the conductor ................................. .................. 36
3.2. Explorer in an external electric field .................................... ... 38
3.3. Conductor electrical capacity ......................................................... 39
3.4. Mutual electrical capacity. Condenters .......................................... 40.
3.5. Constressor connection ............................................................ 41
3.6. Energy of the system of fixed point charges .................. ................. 42
3.7. Own energy charged conductor and condenser ............... 43
3.8. Energy electric field ......................................................................... 44
4. DC laws .................................................................. .45
4.1. The concept of electric current ...................................................... 45
4.2. Ohm's law for a homogeneous section of the chain ....................................... ... 47
Always closed, ... Lecture \u003e\u003e Natural science
No missing. Present course Deals with modern concepts ... The magnetostatic field is generated permanent tokami, the existence of which ... Unlike elektostatiki, consistent the theory of magnetic ... conducting review lectures- Discussions after ...
Methods of application of the COR in the process of studying the topic Electromagnetic oscillations
Coursework \u003e\u003e PedagogyThermodynamics I. molecular physics, electrostatics, optics, atomic and nuclear ... Number of experimental materials. Course "Open Physics 2.0" ... the law established for permanent tok, to describe processes ... Developed in the form lecturessince this ...
Electromotive force.
Ohm's law for a closed chain and an inhomogeneous section of the chain.
Ohm's law for a closed chain says that. The value of the current in the closed circuit, which consists of a current source with internal resistance, as well as external load resistance. Will be equal to attitude electrical power Source to the sum of external and internal resistances.
Ohm law for heterogeneous section of chain
When the electric current is passed in the closed circuit on free charges, the forces on the part of the stationary electric field and third-party power are used. At the same time, in some sections of this circuit, the current is created only by a stationary electric field. Such sections of the chain are called homogeneous. In some areas of this chain, in addition to the power of a stationary electric field, third-party forces act. A section of the chain on which third-party forces act is called an inhomogeneous section of the chain.
In order to find out what the current is depends on these sites, it is necessary to clarify the concept of voltage.
Fig. one
Consider at first a homogeneous section of the chain (Fig. 1, a). In this case, the work on the movement of charge makes only the forces of the stationary electric field, and this area is characterized by the difference in potentials Δφ. Potential difference at the ends of the site 
Where AK is the work of the powerful electric field forces. The inhomogeneous section of the chain (Fig. 1, b) contains as opposed to a homogeneous section of the source of EDC, and the work of third-party forces is added to the operation of the electrostatic field forces. By definition, where q is a positive charge that moves between any two chain points; - the difference in potentials of points at the beginning and end of the section under consideration; . Then they talk about voltages for tension: Estent. e. P. \u003d EE / Stat. p. + Estor. The voltage U on the circuit site is a physical scalar value equal to the total work of third-party forces and forces of the electrostatic field to move a single positive charge on this site:
From this formula, it can be seen that in general, the voltage in this section of the chain is equal to the algebraic amount of the potential difference and the EMF in this area. If only electrical strength (ε \u003d 0) act on the site (ε \u003d 0), then. Thus, only for a homogeneous section of the chain of the concept of voltage and the difference in potentials coincide.
Ohma law for an inhomogeneous section of the chain is:
where R is the overall resistance of the inhomogeneous site.
EMF ε can be both positive and negative. This is due to the polarity of the inclusion of EMF in the area: if the direction generated by the current source coincides with the direction of the current passing in the site (the current direction on the site coincides inside the source with the direction from the negative pole to the positive), i.e. EMF contributes to the movement of positive charges in this direction, then ε\u003e 0, otherwise, if the EMF prevents the movement of positive charges in this direction, then ε< 0.
Rules of Kikhhof.
Work and current power. Thermal current. Law of Joule Lenza.
When current flows over a homogeneous section of the chain, the electric field makes a job. During the time Δ t, the chain flows Δ q \u003d i Δ t. The electric field on the highlighted hassle makes the work
The power of the electric current is equal to the ratio of the current Δ A by the time interval Δ T, for which this work was performed:
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The operation of electric current in Si is expressed in Joules (J), power - in watts (W).
Consider now the complete chain of a DC, consisting of a source with an electromotive force and the inner resistance of R and an external homogeneous area with the resistance R. Ohm's law for the total chain is recorded as
The first term in the left part of Δ q \u003d R i 2 Δ T is a heat released on the external section of the chain during the Δ T, the second term Δ q East \u003d R i 2 Δ T is the heat released inside the source during the same time.
The expression I Δ T is equal to the work of the third-party forces Δ A st, acting within the source.
When the electric current of the closed circuit is flowing, the operation of third-party forces Δ A article is converted to a heat released in the outer chain (Δ q) and inside the source (Δ q East).
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It should be noted that this ratio does not include the operation of the electric field. When the current flow across the closed circuit, the electrical field of operation does not perform; so heat is made only by third-party forces.acting inside the source. The role of the electric field is reduced to the redistribution of heat between different parts of the chain.
The outer chain can be not only a conductor with resistance R, but also any device that consumes power, for example, a DC motor. In this case, under R need to understand Equivalent load resistance. Energy secreted in an external chain can be partially or completely converted not only to heat, but also to other types of energy, for example, in mechanical workMade by the electric motor. Therefore, the question of using the energy source energy is of great practical importance.
