4 Energy Consideration

Energy Consideration

Let ‘r’ be the resistance of movable arm PQ of the rectangular conductor. We assume that the remaining arms QR, RS, and SP have negligible resistances compared to r. Thus, the overall resistance of the rectangular loop is r and this does not change as PQ is moved.

Current I in the loop is,

Due to the presence of the magnetic field, there is a force on the arm PQ. This force is directed outwards in the direction opposite to the velocity of the rod. The magnitude of this force is,

Alternatively, the arm PQ is being pushed with a constant speed v. The power required to do this is,

The agent that does this work is mechanical. This mechanical energy is dissipated as joule heat and is given by,

This is identical to equation (ii).
Thus, mechanical energy, which was required to move the arm PQ, is converted into electrical energy and then to thermal energy.