Derivation of Faraday’s Law

Let us arrange an apparatus as shown in figure 16. It consists of a pair of parallel bare conductors which are spaced l meters apart in uniform magnetic field of ‘B’. We can hold another bare conductor in such a way that it is in contact with the two parallel wires(see figure-16). A galvano meter is connected to the ends of parallel conductors to complete an electric circuit. Now if the cross wire (cross conductor) placed across parallel conductors is moved to the left, galvanometer needle will deflect in one direction.

If this cross wire is moved to the right, its needle deflects in a direction opposite to the previous deflection. Suppose that the crosswire is moved to the left to a distance of ‘s’ meters in a time of ‘Δ t’. Then the reading of galvanometer gives us the amount of current that flows in the circuit. A current will be set up in the circuit only when there is an EMF in the circuit. Let this EMF be ‘ε’. The principle of conservation of energy tells us that this electric energy (associated with flow of current) must come from the work that we have done in moving the crosswire. If we ignore friction everywhere, in the arrangement, the work done by this applied force = Fs. It is evident that there is a current of ‘I’ amperes flowing through the length of l meters of the cross wire, and the cross wire is in a magnetic