How are voltage and induced emf related? What is induced emf and when does it occur? Induction emf in a straight conductor moving in a magnetic field

So, we have established that during the induction process e is excited. d.s. induction, due to which a current arises in the conductors, the strength of which is determined by Ohm’s law through e. d.s. induction and circuit resistance. What is determined by e. d.s. induction?

If you look closely at everyone induction experiments(§ 137), then it is easy to discover that the strength of the induction current in the circuit, and therefore the e. d.s. induction turns out to be different depending on whether we make the change quickly or slowly magnetic flux, which is a necessary condition for the occurrence of induction. The slower the process of changing the magnetic flux occurs, the less e. d.s. induction and the less induced current at a given circuit resistance. Thus, carrying out a certain change in magnetic flux over different times, we get different e. d.s. induction. If at the moment the magnetic flux had a value, and by the moment its value became equal, then during the time there was a change in the magnetic flux by . The ratio gives the change in magnetic flux per unit time, i.e. it represents the rate of change of magnetic flux. Measurements taken at different conditions experience (in any circuit, with any change in the value of the magnetic flux, etc.), show that e. d.s. induction depends only on the rate of change of magnetic flux. Namely:

E.m.f. induction is proportional to the rate of change of magnetic flux through a surface bounded by a contour, and in SI the proportionality coefficient equal to one, So

It goes without saying that if the magnetic flux changes unevenly over time, then the ratio gives an average rate of change of magnetic flux similar to average speed movement (see Volume I), and in accordance with this, formula (141.1) makes it possible to calculate the average e. d.s. induction. To determine the instantaneous value of e. d.s. induction at each moment of time, it is necessary, just as when determining the speed of uneven movement, to consider the change in magnetic flux over such a short period of time that during this period it is possible, with our measurement methods, to consider the change in magnetic flux to be uniform. In such cases, the ratio will characterize the rate of change of magnetic flux for at this moment, and the value calculated based on formula (141.1) will be the value of e. d.s. induction for this moment. All these arguments exactly repeat the arguments related to the definition of instantaneous and average speed in mechanics.

In our reasoning, we assumed that we were dealing with a contour consisting of only one turn, that is, with a contour that once covers the field lines. In general, when induction coil has identical turns, each of which experiences a change in flux, e. d.s. The induction is obviously several times greater, because the turns of the coil are connected to each other in series and e.g. d.s. arising in each of the turns add up. Thus, e. d.s. The induction arising in a coil of turns is proportional to the number of turns and the rate of change of the magnetic flux through each turn of the coil:

In case the turns are unequal, so that the changes in magnetic flux through the individual turns are equal , the sum is the total change in flux passing through all turns of the coil, i.e., the change in flux through the coil as a whole. E.m.f. such a coil

Formulas (141.1) and (141.2) give the value of e. d.s. induction. As for the direction of e. d.s. induction (direction of induced current), then it is determined by Lenz’s rule (§ 139).

The SI unit of magnetic flux is the Weber (Wb), named after the German physicist Wilhelm Eduard Weber (1804-1891). One weber represents the flow through a surface whose area is equal to one square meter, intersected by lines perpendicular to it uniform field with magnetic induction equal to one tesla. At a rate of change of flow equal to 1 Vb/s, e is induced in the circuit. d.s. equal to 1 V.

141.1. In Fig. 267 shows the so-called “earth inductor”. This is a reel from large number turns of wire, which can be brought into fast rotation around the axis coinciding with its vertical diameter. When this coil rotates in the Earth's magnetic field, an inductive effect appears in it. electricity. Consider the following three cases: a) the inductor rotates about vertical axis; b) the axis of rotation is horizontal and directed along the magnetic meridian (from north to south); c) the axis of rotation is horizontal and directed perpendicular to the magnetic meridian (from west to east). Which component of the earth's magnetic field causes induction in each of these cases? In what case is the induced current with other equal conditions will be the largest? If the inclination is this place The Earth's angle is 70°, then in which of the cases - a) or b) - will the induction current be greater?

Rice. 267. For exercise 141.1

141.2. The earth's inductor coil contains 500 turns, the area of ​​each turn is 1200. The inductor rotates at a frequency of 20 rps. Knowing that the horizontal component of induction earth's field at a given location is equal to T and that the inclination is 60°, calculate for each of the cases examined in the previous problem the average value of e. d.s. induction and maximum value flux of magnetic induction through one turn of the coil.

141.3. In a coil without an iron core, having a length of 25 cm and a diameter of 10 cm and containing 1000 turns, the current increases uniformly by 1 A in 1 s. This coil is topped with another coil containing 100 turns. What e. d.s. will be induced in it?

141.4. A coil consisting of 100 turns of wire with a turn radius of 1 cm is placed between the poles of an electromagnet. Its ends are connected to a measuring device, which showed that when the coil is removed from the field or the electromagnet is turned off, an induced charge of 6.28 μC flows in the coil. The coil resistance is 50 ohms, the galvanometer resistance is 1550 ohms. Calculate the magnetic induction in the interpolar space of the electromagnet.

141.5. A coil having a resistance of 1000 Ohms and consisting of 100 turns with an area of ​​5 , was brought into a uniform field between the poles of the electromagnet so that the magnetic field lines turned out to be perpendicular to the plane of the coil turns. At the same time, a charge of 2 μC was induced in it. Calculate the magnetic induction in the interpolar space of the magnet.

141.6. What charge will be induced in the coil previous task, if we rotate it in the interpolar space of the electromagnet so that the plane of its turns makes an angle of 30° with the field lines?

The cause of the electromotive force can be a change in the magnetic field in the surrounding space. This phenomenon is called electromagnetic induction. Magnitude induced emf in the circuit is determined by the expression

where is the magnetic field flux through a closed surface bounded by a contour. The “−” sign before the expression shows that the induced current created by the induced emf prevents a change in the magnetic flux in the circuit (see Lenz’s rule).

41. Inductance, its SI unit. Inductance of a long solenoid.

Inductance(or self-induction coefficient) - proportionality coefficient between electrical electric shock, flowing in some closed loop, and magnetic flux created by this current through the surface , the edge of which is this contour. .

In the formula

Magnetic flux, - current in the circuit, - inductance.

People often talk about the inductance of a straight long wire( cm.).

In this case and other cases (especially in those that do not correspond to the quasi-stationary approximation) when a closed loop is not easy to adequately and unambiguously indicate, the above definition requires special clarification; The approach (mentioned below) that relates inductance to magnetic field energy is partly useful for this. Expressed through inductance Self-induced emf :

.

in a circuit that occurs when the current in it changes Expressed through inductance From this formula it follows that the inductance is numerically equal

, which occurs in the circuit when the current changes by 1 A in 1 s. For a given current, inductance determines energy :

magnetic field created by this current

Designation and units of measurement In the SI system of units, inductance is measured in henry, abbreviated Hn, in GHS system

- in centimeters (1 Gn = 10 9 cm). A circuit has an inductance of one henry if, when the current changes by one ampere per second, a voltage of one volt appears at the terminals of the circuit. A real, non-superconducting circuit has an ohmic resistance R, so an additional voltage U=I*R will appear on it, where I is the current flowing through the circuit at a given instant of time. The symbol used to denote inductance was taken in honor of Lenz Emil Christianovich (Heinrich Friedrich Emil Lenz) [ source not specified 1017 days The symbol used to denote inductance was taken in honor of Lenz Emil Christianovich (Heinrich Friedrich Emil Lenz) [ ] .

An electric current that flows in a closed circuit creates a magnetic field around itself, the induction of which, according to the Biot-Savart-Laplace law, is proportional to the current. The magnetic flux Ф associated with the circuit is therefore directly proportional to the current I in the circuit: (1) where the proportionality coefficient L is called circuit inductance. When the current strength changes in the circuit, the magnetic flux associated with it will also change; This means that an emf will be induced in the circuit. Emergence of e.m.f. induction in a conducting circuit when the current strength changes in it is called self-induction. From expression (1) the inductance unit is specified Henry(H): 1 H - the inductance of a circuit whose self-induction magnetic flux at a current of 1 A is equal to 1 Wb: 1 Hn = 1 Wb/s = 1 V

Let's calculate the inductance of an infinitely long solenoid. The total magnetic flux through the solenoid (flux linkage) is equal to μ 0 μ(N 2 I/ l)S. Substituting in (1), we find (2) i.e. the inductance of the solenoid depends on the length l solenoid, the number of its turns N, its area S and the magnetic permeability μ of the substance from which the solenoid core is made. It has been proven that the inductance of a circuit depends in the general case only on the geometric shape of the circuit, its dimensions and the magnetic permeability of the medium in which it is located, and it is possible to draw an analogue of the inductance of a circuit with the electrical capacitance of a solitary conductor, which also depends only on the shape of the conductor, its dimensions and dielectric constant of the medium. Let us find, applying Faraday’s law to the phenomenon of self-induction, that the emf. self-induction is equal to If the circuit does not undergo deformation and the magnetic permeability of the medium remains unchanged (later it will be shown that the last condition is not always satisfied), then L = const and (3) where the minus sign, determined by Lenz’s rule, indicates that the presence of inductance in the circuit slows down the change in current in it. If the current increases over time, then (dI/dt<0) и ξ s >0 i.e. the self-induction current is directed towards the current caused by the external source and slows down its increase. If the current decreases with time, then (dI/dt>0) and ξ s<0 т. е. индукционный ток имеет такое же направление, как и уменьшающийся ток в контуре, и замедляет его уменьшение. Значит, контур, обладая определенной индуктивностью, имеет электрическую инертность, заключающуюся в том, что любое изменение тока уменьшается тем сильнее, чем больше индуктивность контура.

42. Current when opening and closing a circuit.

With any change in current strength in a conducting circuit, an e occurs. d.s. self-induction, as a result of which additional currents appear in the circuit, called extra currents of self-induction. Extra currents of self-induction, according to Lenz's rule, are always directed so as to prevent changes in the current in the circuit, that is, they are directed opposite to the current created by the source. When the current source is turned off, the extra currents have the same direction as the weakening current. Consequently, the presence of inductance in the circuit slows down the disappearance or establishment of current in the circuit.

Let us consider the process of turning off the current in a circuit containing a current source with an emf. , resistance resistor R and an inductor L. Under the influence of external e. d.s. direct current flows in the circuit

(we neglect the internal resistance of the current source).

At a moment in time t=0 turn off the current source. Current in the coil inductance L will begin to decrease, which will lead to the emergence of emf. self-induction preventing, according to Lenz's rule, a decrease in current. At each moment of time, the current in the circuit is determined by Ohm's law I= s / R, or

Dividing the variables in expression (127.1), we obtain Integrating this equation over I(from I 0 to I) And t(from 0 to t), find ln ( I /I 0) = – Rt/ L, or

where = L/ R - constant called time of relaxation. From (127.2) it follows that  is the time during which the current strength decreases by e times.

Thus, in the process of turning off the current source, the current strength decreases according to the exponential law (127.2) and is determined by the curve 1 in Fig. 183. The greater the inductance of the circuit and the lower its resistance, the greater  and, therefore, the slower the current in the circuit decreases when it opens.

When the circuit is closed, in addition to the external e. d.s. arises e. d.s. self-induction preventing, according to Lenz's rule, an increase in current. According to Ohm's law, or

By introducing a new variable, we transform this equation to the form

where  is the relaxation time.

At the moment of closure ( t=0) current I = 0 and u= –. Therefore, integrating over And(from to IR– ) And t(from 0 to t), find ln[( IR– )]/–= - t/  , or

where is the steady current (at t).

Thus, during the process of turning on the current source, the increase in current strength in the circuit is given by function (127.3) and is determined by curve 2 in Fig. 183. The current increases from the initial value I= 0 and asymptotically tends to the steady-state value . The rate of current rise is determined by the same relaxation time  = L/ R, the same as the decrease in current. The establishment of current occurs the faster, the lower the inductance of the circuit and the greater its resistance.

Let's estimate the value of emf. self-induction, which occurs with an instantaneous increase in the resistance of the DC circuit from R 0 to R. Let us assume that we open the circuit when a steady current flows in it. When the circuit is opened, the current changes according to formula (127.2). Substituting into it the expression for I 0 and  , we get

E.m.f. self-induction

i.e. with a significant increase in circuit resistance (R/ R 0 >>1), with high inductance, emf. self-induction can be many times higher than the emf. current source included in the circuit. Thus, it is necessary to take into account that a circuit containing inductance cannot be abruptly opened, since this (the occurrence of significant self-induction emf) can lead to insulation breakdown and failure of measuring instruments. If resistance is gradually introduced into the circuit, then the emf. self-induction will not reach large values.

43. The phenomenon of mutual induction. Transformer.

Let's consider two fixed contours (1 and 2), which are located quite close to each other (Fig. 1). If a current I 1 flows in circuit 1, then the magnetic flux that is created by this current (the field creating this flux is shown in the figure with solid lines) is directly proportional to I 1 . Let us denote by Ф 21 the part of the flow that penetrates circuit 2. Then (1) where L 21 is the proportionality coefficient.

Fig.1

If the current I 1 changes its value, then an emf is induced in circuit 2. ξ i2, which, according to Faraday’s law, will be equal and opposite in sign to the rate of change of magnetic flux Ф 21, which is created by the current in the first circuit and penetrates the second: Similarly, when current I 2 flows in circuit 2, the magnetic flux (its field is shown in Fig. 1 with strokes) penetrates the first contour. If Ф 12 is part of this flow that permeates circuit 1, then if the current I 2 changes its value, then an emf is induced in circuit 1. ξ i1, which is equal and opposite in sign to the rate of change of magnetic flux Ф 12, which is created by the current in the second circuit and penetrates the first: The phenomenon of emf occurrence. in one of the circuits when the current strength changes in the other is called mutual induction. The proportionality coefficients L 21 and L 12 are called mutual inductance of the circuits. Calculations, which are confirmed by experience, show that L 21 and L 12 are equal to each other, i.e. (2) The proportionality coefficients L 12 and L 21 depend on the size, geometric shape, relative position of the circuits and on the magnetic permeability of the medium surrounding the circuits . The unit of mutual inductance is the same as for inductance, henry (H). Let's find the mutual inductance of two coils that are wound on a common toroidal core. This case is of great practical importance (Fig. 2). Magnetic induction of the field, which is created by the first coil with the number of turns N 1, current I 1 and magnetic permeability μ of the core, B = μμ 0 (N 1 I 1 / l) Where l- length of the core along the midline. Magnetic flux through one turn of the second coil Ф 2 = BS = μμ 0 (N 1 I 1 / l)S

This means that the total magnetic flux (flux linkage) through the secondary winding, which contains N 2 turns, Flux Ψ is created by current I 1, therefore, using (1), we find (3) If we calculate the magnetic flux that is created by coil 2 through coil 1, then for L 12 we obtain an expression in accordance with formula (3). This means that the mutual inductance of two coils, which are wound on a common toroidal core,

Transformer(from lat. transformo- transform) is a static electromagnetic device having two or more inductively coupled windings on any magnetic circuit and intended to be transformed through electromagnetic induction one or more AC systems (voltages) to one or more other AC systems (voltages) without changing the frequency of the AC system (voltages)

Electromagnetic induction is the generation of electric currents by magnetic fields that change over time. Faraday and Henry's discovery of this phenomenon introduced a certain symmetry into the world of electromagnetism. Maxwell managed to collect knowledge about electricity and magnetism in one theory. His research predicted the existence electromagnetic waves before experimental observations. Hertz proved their existence and opened the era of telecommunications to humanity.

Jpg?.jpg 600w, https://elquanta.ru/wp-content/uploads/2018/03/1-14-210x140..jpg 614w" sizes="(max-width: 600px) 100vw, 600px">

Faraday's experiments

Faraday and Lenz's laws

Electric currents create magnetic effects. Is it possible for a magnetic field to generate an electric one? Faraday discovered that the desired effects arise due to changes in the magnetic field over time.

When a conductor is crossed by an alternating magnetic flux, an electromotive force is induced in it, causing an electric current. The system that generates the current can be permanent magnet or electromagnet.

Phenomenon electromagnetic induction governed by two laws: Faraday and Lenz.

Lenz's law allows us to characterize the electromotive force with respect to its direction.

Important! The direction of the induced EMF is such that the current caused by it tends to resist the cause that creates it.

Faraday noticed that the intensity of the induced current increases when the number changes faster power lines, crossing the contour. In other words, EMF electromagnetic induction is directly dependent on the speed of the moving magnetic flux.

Jpg?.jpg 600w, https://elquanta.ru/wp-content/uploads/2018/03/2-10-768x454..jpg 960w" sizes="(max-width: 600px) 100vw, 600px">

induced emf

The formula for induced emf is defined as:

E = - dФ/dt.

The "-" sign shows how the polarity of the induced emf is related to the sign of the flux and the changing speed.

A general formulation of the law of electromagnetic induction is obtained, from which expressions for special cases can be derived.

Movement of a wire in a magnetic field

When a wire of length l moves in an MF having induction B, an EMF will be induced inside it, proportional to its linear speed v. To calculate the EMF, the formula is used:

• in the case of conductor movement perpendicular to the direction of the magnetic field:

E = - B x l x v;

• in case of movement at a different angle α:

E = — B x l x v x sin α.

The induced emf and current will be directed in the direction that we find using the rule right hand: placing your hand perpendicular to the magnetic field lines and pointing thumb in the direction of movement of the conductor, you can find out the direction of the EMF by the remaining four straightened fingers.

Jpg?x15027" alt="Moving wire in MP" width="600" height="429">!}

Moving the wire in the MP

Rotating reel

The operation of the electricity generator is based on the rotation of a circuit in the MP having N turns.

EMF is induced in an electrical circuit whenever a magnetic flux crosses it, in accordance with the definition of magnetic flux Ф = B x S x cos α (magnetic induction multiplied by the surface area through which the MF passes and the cosine of the angle, formed by a vector B and a line perpendicular to plane S).

From the formula it follows that F is subject to changes in the following cases:

• MF intensity changes – vector B;
• the area limited by the contour varies;
• the orientation between them, specified by the angle, changes.

In Faraday's first experiments, induced currents were obtained by changing the magnetic field B. However, it is possible to induce an emf without moving the magnet or changing the current, but simply by rotating the coil around its axis in the MF. IN in this case the magnetic flux changes due to the change in angle α. When the coil rotates, it crosses the MF lines, and an EMF occurs.

If the coil rotates uniformly, this periodic change results in periodic change magnetic flux. Or the number of MP field lines crossed every second takes equal values at regular intervals.

Jpg?.jpg 600w, https://elquanta.ru/wp-content/uploads/2018/03/4-10-768x536..jpg 900w" sizes="(max-width: 600px) 100vw, 600px">

Rotation of the contour in MP

Important! The induced emf changes along with the orientation over time from positive to negative and vice versa. Graphical representation EMF is a sinusoidal line.

For EMF formulas electromagnetic induction the following expression is used:

E = B x ω x S x N x sin ωt, where:

• S – area limited by one turn or frame;
• N – number of turns;
• ω – angular velocity, with which the coil rotates;
• B – MP induction;
• angle α = ωt.

In practice, in alternating current generators, the coil often remains stationary (stator) and the electromagnet rotates around it (rotor).

Self-induced emf

When it passes through the coil alternating current, it generates an alternating MF, which has a changing magnetic flux that induces an emf. This effect is called self-induction.

Since the MF is proportional to the current intensity, then:

where L is the inductance (H), determined by geometric quantities: the number of turns per unit length and the dimensions of their cross-section.

For induced emf, the formula takes the form:

E = - L x dI/dt.

Mutual induction

If two coils are located next to each other, then an emf of mutual induction is induced in them, depending on the geometry of both circuits and their orientation relative to each other. As the separation of the circuits increases, the mutual inductance decreases as the magnetic flux connecting them decreases.

Jpg?.jpg 600w, https://elquanta.ru/wp-content/uploads/2018/03/5-5.jpg 680w" sizes="(max-width: 600px) 100vw, 600px">

Mutual induction

Let there be two coils. A current I1 flows through the wire of one coil with N1 turns, creating an MF passing through the coil with N2 turns. Then:

1. Mutual inductance of the second coil relative to the first:

M21 = (N2 x F21)/I1;

1. Magnetic Flux:

F21 = (M21/N2) x I1;

1. Let's find the induced emf:

E2 = - N2 x dФ21/dt = - M21x dI1/dt;

1. An EMF is induced identically in the first coil:

E1 = - M12 x dI2/dt;

Important! The electromotive force caused by mutual induction in one coil is always proportional to the change in electric current in the other.

Mutual inductance can be considered equal to:

M12 = M21 = M.

Accordingly, E1 = - M x dI2/dt and E2 = M x dI1/dt.

M = K √ (L1 x L2),

where K is the coupling coefficient between two inductances.

The phenomenon of mutual induction is used in transformers - electrical devices that allow you to change the value of the voltage of an alternating electric current. The device consists of two coils wound around one core. The current present in the first one creates a changing MF in the magnetic circuit and an electric current in the other coil. If the number of turns of the first winding is less than the other, the voltage increases, and vice versa.

Let us consider, just as when deriving the expression for the work of moving a contour, a flat contour containing an EMF source, one side of which is movable (see Fig. 2).

Source from EMF equal creates a current in the circuit, while developing a power equal to . This power turns into heat according to the Joule-Lenz law. Based on the law of conservation of energy, we write:

Let us now excite a uniform magnetic field directed away from us behind the drawing. The vector coincides with the positive normal to the contour, so the magnetic flux is positive. According to Ampere's law, each element of the circuit will experience a force from the magnetic field. The moving side of the circuit will experience a net force. Let us now allow the movable side to move under the influence of this force to the right with constant speed .

At the same time, since there is a phenomenon of electromagnetic induction (after all, the magnetic flux through a closed circuit changes), the current in the circuit will change and become . The resulting force acting on the moving side will change accordingly. She will become.

This force will do work in time equal to:

But according to Ampere's law, this force is equal to:

Therefore, the expression for the work will take the form:

those. previously obtained result.

As in the case of stationary elements of the circuit, the source of work is the current source, the source of the emf.

In the case of stationary circuit elements, all the work done by the EMF source is converted into heat.

In the case of a moving side, Lenz-Joule heat will also be released, but differently, since . And, in addition, it will also be accomplished mechanical work, the expression for which we defined above.

According to the law of conservation of energy, we must now write:

From here we get:

Comparing the resulting expression with Ohm's law for a complete circuit -, we come to the conclusion that the resulting emf acting in the circuit is equal to:

Thus, we get that the induced emf is equal to:

where the “-” sign reflects Lenz’s rule.

Electronic mechanism for the occurrence of induced emf

Let us again consider the above circuit shown in Fig. 3. But now we will assume that there is no source. Those. there is a circuit with a moving side in a magnetic field (see Fig. 3).

Unlike the previous case, we will move the moving side at a certain speed. In this case, the charges inside the moving side (after all, this is a conductor and there are moving charges in it), will be acted upon by the Lorentz force directed along the conductor:

Comparing this expression with the expression for the force acting on a charge placed in an electric field of intensity -, we come to the conclusion that the action of this Lorentz force is equivalent to the action electric field with tension

This field is not of electrostatic origin, therefore its circulation in a closed loop is different from zero and will give the value of the induced emf:

That is, we got the same result up to a sign.

Let's dwell on some points.

1. We said above that the action of the Lorentz force is equivalent to the action of an electric field.

This is not just a superficial analogy. This conclusion has a deep physical meaning.

In fact, let's move to the reference system associated with the moving conductor. Then we will say that there is no Lorentz force, since the charges in this frame of reference are at rest. But at the same time, there is an electric field, under the influence of which the charges move.

At the same time, we will have to admit that this electric field is due to a moving magnetic field (after all, in this reference frame the magnetic field is moving).

Thus, we are already coming to the conclusion that a changing magnetic field generates an electric field. That is, we come to the idea of ​​​​the relationship between the fields and their inextricable unity.

2. Earlier we emphasized and talked about the fact that the Lorentz force does not produce work.

At the same time, here we consider the induced emf, which is a measure of work based on the expression for the Lorentz force. What's the matter?

The fact is that in the calculations we did not take the entire Lorentz force, but only the longitudinal (along the moving side) component of the force: . In fact, since the charges move along the conductor at an ordered speed (electric current), there is also a transverse component of the Lorentz force (which does not affect the EMF, see Fig. 4). Hence, full strength Lorentz will be equal to:

The expression for the work of this force can be represented as:

The second term is taken with a minus sign, since the force is directed against the speed, against the movement. Substituting the expressions for forces and into the expression for work, we obtain.

The appearance of electromotive force (EMF) in bodies moving in a magnetic field is easy to explain if we recall the existence of the Lorentz force. Let the rod move in a uniform magnetic field with induction Fig. 1. Let the direction of the speed of movement of the rod () and be perpendicular to each other.

Between points 1 and 2 of the rod, an emf is induced, which is directed from point 1 to point 2. The movement of the rod is the movement of positive and negative charges that are part of the molecules of this body. The charges move together with the body in the direction of movement of the rod. The magnetic field affects the charges using the Lorentz force, trying to move positive charges towards point 2, and negative charges to the opposite end of the rod. Thus, the action of the Lorentz force generates an induced emf.

If a metal rod moves in a magnetic field, then positive ions, being in the nodes crystal lattice, cannot move along the rod. In this case, mobile electrons accumulate in excess at the end of the rod near point 1. The opposite end of the rod will experience a shortage of electrons. The voltage that appears determines the induced emf.

If the moving rod is made of a dielectric, the separation of charges under the influence of the Lorentz force leads to its polarization.

The induced emf will be zero if the conductor moves parallel to the direction of the vector (that is, the angle between and is zero).

Induction emf in a straight conductor moving in a magnetic field

We obtain a formula for calculating the induced emf that occurs in straight conductor, having length l, moving parallel to itself in a magnetic field (Fig. 2). Let v - instantaneous speed conductor, then in time it will describe an area equal to:

In this case, the conductor will cross all the lines of magnetic induction that pass through the pad. We obtain that the change in magnetic flux () through the circuit into which the moving conductor enters:

where is the component of magnetic induction perpendicular to the area. Let us substitute the expression for (2) into the basic law of electromagnetic induction:

In this case, the direction of the induction current is determined by Lenz's law. That is, the induced current has such a direction that mechanical force, which acts on the conductor, slows down the movement of the conductor.

Induction emf in a flat coil rotating in a magnetic field

If a flat coil rotates in a uniform magnetic field, the angular velocity of its rotation is equal to , the axis of rotation is in the plane of the coil and , then the induced emf can be found as:

where S is the area limited by the coil; - coil self-induction flux; - angular velocity; () - angle of rotation of the contour. It should be noted that expression (5) is valid when the axis of rotation makes a right angle with the direction of the vector external field.

If the rotating frame has N turns and its self-induction can be neglected, then:

Examples of problem solving

EXAMPLE 1