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Electromagnetic induction

§ 1 The phenomenon of electromagnetic induction.

Faraday's law

  1. Faraday's experiments

a) The solenoid, closed the galvanometer, pushed into and put forward the permanent magnet. The galvanometer deflection will, and it will be longer than the faster the pushed into and put forward. When you change the direction of the poles of the magnet deflection change.

b) solenoid, closed the galvanometer is inserted coil (another solenoid) through which current is passed. When you turn on and off (ie, any change in the current) is deflection of the galvanometer. Direction of the deviation varies with On - Off, decrease - the current increases, vdviganii - sliding out the coils.

The phenomenon of electromagnetic induction is that in a closed conducting circuit when the flow of magnetic induction covered by this contour, an induction (induced) electric current.
Occurrence of the induced current means that the circuit operates electromotive force
Ei - induced emf.



EMF induction, which occurs in the conducting circuit, equal to the rate of change of magnetic flux through the area bounded by this contour - Faraday's law.

In 1834, E.H. Lenz established the law, allowing to determine the direction of induced current.
Lenz rule: induction loop current always has a direction such that the magnetic field created by it prevents the change in magnetic flux that caused this induced current.

The minus sign in Faraday's Law is a mathematical expression of the rule of Lenz.
If the circuit in which the induced emf is not composed of a single turn, and of N turns (eg, solenoid), if windings are connected in series,
Ei will be equal to the emf induced in each of the coils individually:


-flux linkage or the total magnetic flux.


If Ф12=…=Фn, then

Because ФB=BScosα, then in order to change the magnetic flux F can be changed:

1)magnetic field ;

2) the area S;

3) the angle α.

§2 Spin current loop in a magnetic field

The phenomenon of electromagnetic induction is used to convert mechanical energy and the energy of the electric current in the generator current loop area S rotates in a uniform magnetic field ()evenly with a constant angular velocity ω.

α = ωt.


At sin ωt=1


Because network frequency , then for increase

need to increase B and S. As can be increased by using powerful permanent magnets or electromagnets to pass large currents. Core with a large electromagnet choose μ. To increase the use of S multiturn coil.

If a current loop placed in a magnetic field, an electric current, then it will be acted torque

and the current loop starts to rotate. Based on this principle of the motor, designed to transform electrical energy into mechanical energy.

§3 Foucault currents.

Induced currents can be excited in continuous bulk conductors. In this case they are called Foucault currents or eddy currents. The electrical resistance of a bulk conductor is small, so eddy currents can reach a very large force.

Eddy currents, as well as induced currents in linear conductors are subject Lenz's law: their magnetic field is directed so to counteract changes in the magnetic field that induces eddy currents.

Therefore, moving in a strong magnetic field are good conductors under heavy braking due to the interaction of the eddy currents and the magnetic field. It is used for damping (steadying) of moving parts galvanometers, seismographs, etc. Thermal effect of the eddy currents is used in induction melting furnaces.

To reduce eddy currents transformer cores made ??of individual plates and the plates are perpendicular to the currents of Foucault.

S due to eddy currents rapidly current unevenly distributed over the cross section of wire - it pushed to the surface of a conductor - the skin effect. Therefore, at high frequencies using hollow wire.


§ 4 of the circuit inductance.


In any case where the contour of the electric current creates a magnetic field. In this case, there is always a magnetic flux F passing through the surface bounded by the circuit under consideration. Any change in the current in the circuit changes the magnetic field, coupled with the circuit, and this in turn causes the induced current. This phenomenon is called self-induction: the emergence of the emf induced in a conductor when the current in it.

Of the Biot-Savart-Laplace should


ie magnetic flux linked with the circuit is proportional to the current I in the circuit


[L] = H (henry).

1 H - inductance of the loop, the magnetic flux is self-induced by a current of 1 A is 1 Wb


Calculate the inductance L of the solenoid

magnetic induction of the solenoid



ie inductance depends on the geometry of the solenoid (),number of turns and the magnetic permeability of the core solenoid. Therefore we can say that the inductance L capacitance C analogue isolated conductor, which also depends on the geometry, the shape and the dielectric constant of the medium.
Applying the self-induction Faraday's law, we find that self-induced emf

If   L = const

where the minus sign, due to Lenz's law, shows that the presence of inductance in the circuit slows current change in him.

If the current increases with time , then , and  ie current is directed towards the self-inductance of the current, due to the external source and inhibits its growth. If the current time is decreasing, then  and  ie induced current has the same direction as the decreasing current in the circuit, and slows its decay. Consequently, the circuit having inductance is electrically inert, consists in the fact that any change in the current is inhibited, the stronger, the more inductance.










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