Faraday’s Law of Induction

Michel Faraday has elaborated

How a changing magnetic field generates an electric current in a conductor?

Faraday’s Law of Induction

He has stated that the induced voltage in a circuit is proportionate to the rate of change the magnetic flux per time or if the magnetic field changes, induced e.m.f. or voltage will be more and the direction of the change in the magnetic field regulates current’s direction. This is known as Faraday’s law.

Michael Faraday
Michael Faraday, Image By – Thomas PhillipsM Faraday Th Phillips oil 1842, marked as public domain, more details on Wikimedia Commons

Magnetic Flux

Magnetic Flux can be stated mathematically as ΦB = BA cos

A is the surface in which B uniform magnetic field is acting on.
ΦB is the magnetic flux. is the angle between and B and A.

Ways to change the magnetic flux:-

  • From the above equation, it is understandable that the flux could be varied if we change the magnitude magnetic field.
  • The angle in-between magnetic field B and the plane of coil could be changed too, surface area A is also a changeable parameter.

Some important facts about magnetic flux:

  • Magnetic flux is a scalar quantity.
  • S.I unit of Magnetic flux is denoted as weber(Wb)
  • 1 Wb = 1 Tesla.
  • C.G.S unit of magnetic flux is Maxwell.
  • 1Wb = Maxwell.

Now, according to Faraday’s Law of induction, e(t)= ΦB.

In case of a coil of N turns, change of flux with each turn is the same and hence the total induced emf becomes, e(t)= ΦB.

The negative sign specifies the direction of induced emf, which is in accordance with the Lenz’s Law which is stated as follows:

The direction of the emf induced and hence the direction of the induced current in a circuit is to oppose the cause due to which they were produced, i.e. if the flux is increasing, then the induced emf will be produced in such a direction that will try to decrease the flux and vice-versa.

In reality, Lenz’s law is a coincidence of the conservation of energy. As the emf is induced in such a way that it opposes the change in flux, hence work has to be done against this opposition given by the induced emf to ensure that the flux change continues in the same way. This work done appears as electrical energy in the circuit.

From the equations above we can state that the induced emf or the electric current in the circuit can be increased in the following ways:-

  • Changing the flux very rapidly can increase the induced emf.
  • Using a rod of soft iron core inside the coil.
  • Increasing N, i.e., increasing the number of turns of the coil.

As seen in the figure, we can generate an emf when the magnet is placing near to a circuit or when a circuit is placed nearer to a magnet. In these cases, the direction of the induced current is shown.

direction of induced electric field according to Lenz's Law
Direction of induced electric field according to Lenz’s Law

Another way in which emf can be induced is the working principle of AC, where the circuit is a coil of conducting wire circulating in a magnetic field and hence flux ΦB changes in a sinusoidal way in time.

Motional Electromotive Force (an implication of Faraday’s Law of induction)

Faraday's law
Electromotive force induced due to change in area of magnetic flux due to relative motion

The above figure shows a rectangular conductor ABCD upon which a conducting rod EF moves with constant velocity. The magnetic field is perpendicular, i.e., inwards to the plane of the closed conducting loop ABFE. 

The magnetic flux enclosed by the loop at time t = t s is,

ΦB(t)= = BA=Blx(t),

The time rate of change of this flux, induces an emf given by e= ΦB = (-Blx(t))= Bl.x(t) = Blv.                                                                                                                          

This electromotive force obtained due to the motion of the conductor EF instead of changing the magnetic field is known as a motional electromotive force.

Electromagnetic induction explains the induction of currents and voltages as a coincidence of changing magnetic fields. But the more modern view states that the induction occurs even in the absence of a conducting wire or any material medium.