# Faraday Law of Electromagnetic Induction

In 1831, Michael Faraday, an English physicist gave one of the most basic laws of electromagnetism called Faraday's law of electromagnetic induction. This law explains the working principle of most of the electrical motors, generators, electrical transformers and inductors. This law shows the relationship between electric circuit and magnetic field. Faraday performs an experiment with a magnet and coil. During this experiment, he found how emf is induced in the coil when flux linked with it changes. He has also done experiments in electro-chemistry and electrolysis.

RELATIONSHIP BETWEEN INDUCED EMF AND FLUX

In this experiment, Faraday takes a magnet and a coil and connects a galvanometer across the coil. At starting, the magnet is at rest, so there is no deflection in the galvanometer i.e needle of galvanometer is at the center or zero position. When the magnet is moved towards the coil, the needle of galvanometer deflects in one direction. When the magnet is held stationary at that position, the needle of galvanometer returns back to zero position. Now when the magnet is moved away from the coil, there is some deflection in the needle but in opposite direction and again when the magnet becomes stationary, at that point with respect to coil, the needle of the galvanometer returns back to the zero position. Similarly, if magnet is held stationary and the coil is moved away and towards the magnet, the galvanometer shows deflection in similar manner. It is also seen that, the faster the change in the magnetic field, the greater will be the induced emf or voltage in the coil.

Conclusion: From this experiment, Faraday concluded that whenever there is relative motion between conductor and a magnetic field, the flux linkage with a coil changes and this change in flux induces a voltage across a coil.

Michael Faraday formulated two laws on the basis of above experiments. These laws are called Faraday's laws of electromagnetic induction.

Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.

1. Method to change magnetic field:By moving a magnet towards or away from the coil
2. By moving the coil into or out of the magnetic field.
3. By changing the area of a coil placed in the magnetic field
4. By rotating the coil relative to the magnet.

It states that the magnitude of emf induced in the coil is equal to the rate of change of fluxthat linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.

Consider a magnet approaching towards a coil. Here we consider two instants at time T1and time T2. Flux linkage with the coil at time, T1 = NΦ1 Wb

Flux linkage with the coil at time, T2 = NΦ2 wb

Change in flux linkage = N(Φ2 - Φ1)

Let this change in flux linkage be, Φ = Φ2 - Φ1

So, the Change in flux linkage = NΦ

Now the rate of change of flux linkage = NΦ / t

Take derivative on right hand side we will get

The rate of change of flux linkage = NdΦ/dt

But according to Faraday's law of electromagnetic induction, the rate of change of flux linkage is equal to induced emf.

Considering Lenz's Law.

Where, flux Φ in Wb = B.A

B = magnetic field strength

A = area of the coil

• HOW TO INCREASE EMF INDUCED IN A COILBy increasing the number of turns in the coil i.e N- From the formulae derived above it is easily seen that if number of turns of coil is increased, the induced emf also gets increased.
• By increasing magnetic field strength i.e B surrounding the coil- Mathematically if magnetic field increases, flux increases and if flux increases emf induced will also get increased. Theoretically, if the coil is passed through a stronger magnetic field, there will be more lines of force for coil to cut and hence there will be more emf induced.
• By increasing the speed of the relative motion between the coil and the magnet - If the relative speed between the coil and magnet is increased from its previous value, the coil will cut the lines of flux at a faster rate, so more induced emf would be produced.