What is the induction emf of moving conductors? Movement of a conductor in a magnetic field

Or, conversely, a moving magnetic field crosses a stationary conductor; or when a conductor and a magnetic field, moving in space, move relative to each other;

When an alternating magnetic field of one conductor, acting on another conductor, induces an EMF in it (mutual induction);

When a changing magnetic field induces an EMF (self-induction) in it itself.

Thus, any change in time of the value penetrating a closed circuit (turn, frame) is accompanied by the appearance of an induced emf in the conductor.

A = U × I × t = I² × r × t(J) .

The power consumed will be equal to:

P el = U × I = I² × r(W)

from where we determine the current in the circuit:

(1)

However, we know that a current-carrying conductor placed in a magnetic field will experience a force from the field, tending to move in the direction determined by the left-hand rule. During its movement, the conductor will cross the magnetic field lines and, according to the law of electromagnetic induction, an induced emf will arise in it. The direction of this EMF, determined by the right-hand rule, will be opposite to the current I. Let's call it back EMF E arr. Magnitude E arr according to the law of electromagnetic induction will be equal to:

E arr = B × l × v(IN) .

For a closed circuit we have:

U - E arr = I × r

U = E arr + I × r ,

(2)

where does the current in the circuit come from?

(3)

Comparing expressions (1) and (3), we see that in a conductor moving in a magnetic field, at the same values U And r the current will be less than with a stationary conductor.

Multiplying the resulting expression (2) by I, we get:

U × I = E arr × I + I² × r .

Because E arr = B × l × v, That

U × I = B × l × v × I + I² × r .

Considering that B × l × I = F And F × v = P fur, we have:

U × I = F × v + I² × r

P = P fur + P Em.

The last expression shows that when a current-carrying conductor moves in a magnetic field, the power of the voltage source is converted into thermal and mechanical power.

A metal conductor contains a large number of free electrons that move randomly. If you move a conductor in a magnetic field perpendicular to the lines of force, then the field will deflect the electrons moving with the conductor, and they will begin to move, that is, a electromotive force (EMF). It's called electromagnetic induction(induce - induce).

Under the influence of EMF, electrons will move and accumulate at one end of the conductor, and at the other there will be a lack of electrons, that is, a positive charge will arise potential difference, or electrical voltage.

If you connect such a conductor to an external circuit (close the path), then current will flow under the influence of the potential difference.

If the conductor is moved along the lines of force, then the field will not act on the charges, the EMF, the voltage will not arise, and the current will not flow.

This EMF is called induced emf. It is determined by Faraday's law:

· induced emf equal to the product of the speed of movement of the conductor V, magnetic induction IN and active conductor length L

Its direction is determined by right hand rule:

·
If the right hand is placed in a magnetic field so that the lines of force enter the palm, and the bent thumb shows the direction of movement of the conductor, then four extended fingers will show the direction of the EMF.

EMF will be induced at any intersection of the conductor and the magnetic field. That is, you can move the conductor, you can move the field, or you can change the magnetic field.

Then the emf is determined according to Maxwell:

The EMF induced in the circuit as a result of its intersection with a changing magnetic flux is equal to the rate of change of this flux.

e= - ΔФ/Δt

Where ΔФ=Ф 1 - Ф 2 change in magnetic flux, Wb

Δt – time during which the magnetic flux changed, sec.

Lenz's rule: The induced emf is in such a direction that the current it creates opposes the change in magnetic flux.

Self-induced emf.

If the current in a conductor changes, the magnetic flux created by it also changes. Propagating in space, this magnetic flux crosses not only neighboring conductors, but also its own, which means that an EMF is induced in its own conductor. It's called Self-induced emf.

Self-induced emf is the emf that occurs in a conductor when its own current and magnetic flux change.

It occurs with any change in current and is directed so as to prevent it from changing. When the current decreases, it is directed along with it and supports the current; when the current increases, it is directed against it and weakens it.

The ability of a conductor (coil) to create a self-inductive emf is called inductance L.

It depends on:

Square of the number of turns of the coil w

magnetic permeability µ

· coil cross-section S

· coil length l

L=(w 2 μS)/l, Gn(Henry)

Self-induced emf:

e L =-Δi/Δt , V

Where Δi/Δt is the rate of change of current.

This EMF, preventing a change in current, prevents it from flowing, and therefore creates resistance to alternating current.

Switching overvoltages.

These are overvoltages in circuits with high inductance during switching. As a result, an electric arc or spark may occur and the contacts will melt. Therefore, arc suppression measures are applied.

Mutual induction.

EMF mutual induction- this is the emf that occurs in a coil when it is crossed by a changing magnetic flux of another coil.

A transformer operates on this principle.

Induced voltage – This is the voltage that occurs in metal structures as a result of their intersection with an alternating magnetic field created by alternating current.

Thus, due to the magnetic field, three types of EMF arise:

1. induced emf. Occurs when a conductor moves in a constant magnetic field, or when the field moves relative to the conductor.

2. Self-induced emf. It occurs due to the intersection of a conductor with its own changing magnetic field.

3. EMF mutual induction. Occurs when a conductor is crossed by someone else's changing magnetic field.

Eddy currents.

In other words: Foucault currents, induction currents.

These are currents arising in massive steel parts of electrical installations (cores, housings) due to their intersection with a changing magnetic flux and the induction of EMF. As a result of low resistance, the resulting short-circuited currents greatly heat up the machines.

Eddy current losses are power losses due to heating.

To reduce losses, reduce eddy currents as follows:

1. The cores of electric machines are made laminated, that is, they are assembled from sheets of electrical steel insulated with varnish. This reduces the cross-section and therefore increases the current resistance.

2. Silicon, which has high resistance, is added to steel.

After clarifying the nature of the induced emf that occurs in a stationary conductor located in a changing magnetic field, we learned about the properties of the electric field, which differs from that created by point charges. We also learned that work along a closed loop in a field created by point charges is zero, but in a vortex field it is not zero. It is this field that causes EMF in the conductor. However, if the conductor moves in a constant magnetic field, a potential difference will arise at the ends of the conductor, and an EMF will also arise there. But the nature of this force will be different. In this lesson we will find out the nature of the EMF in a conductor moving in a magnetic field.

Subject:Electromagnetic induction

Lesson:Movement of a conductor in a magnetic field

In order to establish the nature of the force in a conductor that moves in a magnetic field, we will conduct an experiment. Let us assume that in a vertical uniform magnetic field with induction () there is a horizontal conductor of length ( l), which moves at a constant speed () perpendicular to the magnetic induction vector of the magnetic field. If we connect a sensitive voltmeter to the ends of this conductor, we will see that it will show the presence of a potential difference at the ends of this conductor. Let's find out where this tension comes from. In this case, there is no loop and no changing magnetic field, so we cannot say that the movement of electrons in the conductor arose as a result of the appearance of a vortex electric field. When the conductor moves as a single whole (Fig. 1), the charges of the conductor and the positive ions that are located in the nodes of the crystal lattice, and the free electrons, have a speed of directional movement.

Rice. 1

These charges will be acted upon by the Lorentz force from the magnetic field. According to the “left hand” rule: four fingers located in the direction of movement, turn the palm so that the magnetic induction vector enters the back side, then the thumb will indicate the action of the Lorentz force on positive charges.

The Lorentz force acting on charges is equal to the product of the modulus of the charge that it transfers, multiplied by the modulus of magnetic induction, by the speed and the sine of the angle between the magnetic induction vector and the velocity vector.

This force will do work to transfer electrons over short distances along the conductor.

Then the total work done by the Lorentz force along the conductor will be determined by the Lorentz force multiplied by the length of the conductor.

The ratio of the work done by an external force to move a charge to the amount of charge transferred, as determined by EMF.

(4)

So, the nature of the occurrence of induced emf is the work of the Lorentz force. However, formula 10.4. can be obtained formally, based on the definition of the EMF of electromagnetic induction, when a conductor moves in a magnetic field, crossing lines of magnetic induction, covering a certain area, which can be defined as the product of the length of the conductor and the displacement, which can be expressed in terms of the speed and time of movement. The induced emf in magnitude is equal to the ratio of the change in magnetic flux to time.

The magnetic induction module is constant, but the area that covers the conductor changes.

After substitution, the expressions in formula 10.5. and the abbreviations we get:

The Lorentz force acting along the conductor, due to which the redistribution of charges occurs, is only one component of the forces. There is also a second component, which arises precisely as a result of the movement of charges. If electrons begin to move along a conductor, and the conductor is in a magnetic field, then the Lorentz force begins to act, and it will be directed against the movement of the conductor’s speed. Thus, the summing Lorentz force will be equal to zero.

The resulting expression for the induced emf that occurs when a conductor moves in a magnetic field can also be obtained formally, based on the definition. The induced emf is equal to the rate of change of magnetic flux per unit time, taken with a minus sign.

When a stationary conductor is in a changing magnetic field and when the conductor itself moves in a constant magnetic field, the phenomenon occurs electromagneticinduction. In both cases, an induced emf occurs. However, the nature of this force is different.

1. Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 pp.: ill., 8 l. color on
2. Tikhomirova S.A., Yarovsky B.M., Physics 11. - M.: Mnemosyne.
3. Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.

1. Fizportal.ru ().
2. Eduspb.com ().
3. Cool physics ().

Homework

1. Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 pp.: ill., 8 l. color on, st. 115, z. 1, 3, 4, art. 133, z. 4.
2. A vertical metal rod 50 cm long moves horizontally at a speed of 3 m/s in a uniform magnetic field with an induction of 0.15 Tesla. The magnetic field induction lines are directed horizontally at right angles to the direction of the rod's velocity vector. What is the induced emf in the rod?
3. At what minimum speed must a rod 2 m long be moved in a uniform magnetic field with a magnetic induction of 50 mT in order for an induced emf of 0.6 V to arise in the rod?
4. * A square made of a 2 m long wire moves in a uniform magnetic field with an induction of 0.3 Tesla (Fig. 2). What is the induced emf on each side of the square? Total induced emf in the circuit? υ = 5 m/s, α = 30°.

When a straight conductor moves in a magnetic field, e.m. occurs at the ends of the conductor. d.s. induction. It can be calculated not only by the formula, but also by the formula e. d.s.

induction in a straight conductor. It comes out like this. Let us equate formulas (1) and (2) § 97:

BIls = EIΔt, from here

Where s/Δt=v is the speed of movement of the conductor. Therefore e. d.s. induction when the conductor moves perpendicular to the magnetic field lines

E = Blv.

If the conductor moves with a speed v (Fig. 148, a), directed at an angle α to the induction lines, then the speed v is decomposed into components v 1 and v 2. The component is directed along the induction lines and does not cause emission in it when the conductor moves. d.s. induction. In the conductor e. d.s. is induced only due to the component v 2 = v sin α, directed perpendicular to the induction lines. In this case e. d.s. induction will be

E = Blv sin α.

This is the formula e. d.s. induction in a straight conductor.

So, When a straight conductor moves in a magnetic field, an e is induced in it. d.s., the value of which is directly proportional to the active length of the conductor and the normal component of the speed of its movement.

If instead of one straight conductor we take a frame, then when it rotates in a uniform magnetic field, an e will appear. d.s. on its two sides (see Fig. 138). In this case e. d.s. induction will be E = 2 Blv sin α. Here l is the length of one active side of the frame. If the latter consists of n turns, then e occurs in it. d.s. induction

E = 2nBlv sin α.

What uh. d.s. induction depends on the speed v of rotation of the frame and on the induction B of the magnetic field, which can be seen in this experiment (Fig. 148, b). When the armature of the current generator rotates slowly, the light bulb lights up dimly: a low emission has occurred. d.s. induction. As the speed of rotation of the armature increases, the light bulb burns brighter: a larger e occurs. d.s. induction. At the same speed of armature rotation, we remove one of the magnets, thereby reducing the magnetic field induction. The light is dimly lit: eh. d.s. induction decreased.

Problem 35. Straight conductor length 0.6 m connected to a current source by flexible conductors, e.g. d.s. whom 24 V and internal resistance 0.5 ohm. The conductor is in a uniform magnetic field with induction 0.8 tl, the induction lines of which are directed towards the reader (Fig. 149). Resistance of the entire external circuit 2.5 ohm. Determine the current strength in the conductor if it moves perpendicular to the induction lines at speed 10 m/sec. What is the current strength in a stationary conductor?

The relationship between electrical and magnetic phenomena has always interested physicists. English physicist Michael Faraday was completely confident in the unity of electrical and magnetic phenomena. He reasoned that an electric current could magnetize a piece of iron. Couldn't a magnet in turn cause an electric current? This problem has been solved.

If a conductor moves in a constant magnetic field, then the free electric charges inside it also move (they are acted upon by the Lorentz force). Positive charges are concentrated at one end of the conductor (wire), negative charges at the other. A potential difference arises - EMF electromagnetic induction. The phenomenon of induced emf in a conductor moving in a constant magnetic field is called phenomenon of electromagnetic induction.

Rule for determining the direction of induction current (right hand rule):

In a conductor moving in a magnetic field, an induced emf occurs; the current energy in this case is determined according to the Joule-Lenz law:

Work done by an external force to move a current-carrying conductor in a magnetic field

Induction EMF in the circuit

Let's consider the change in magnetic flux through a conducting circuit (coil). The phenomenon of electromagnetic induction was discovered experimentally:

Law of electromagnetic induction (Faraday's law): The electromagnetic induction emf arising in the circuit is directly proportional to the rate of change of the magnetic flux through it.