Define : (i) Self inductance (ii) Mutual inductanceA conducting loop of area 1 m\(^2\) is placed normal to a uniform magnetic field of 3 Wb/m\(^2\). If the magnetic field is uniformly reduced to 1 Wb/m\(^2\) in 0.5 second, calculate the induced e.m.f…

Answer: Definitions below; induced e.m.f. = 4 V.

(i) Self inductance: The magnetic flux linked with a coil is proportional to the current in it, \(N\Phi = LI\). The self inductance \(L\) of a coil is the flux linkage per unit current in it, or equivalently the e.m.f. induced in the coil per unit rate of change of current in the same coil: \(e = -L\dfrac{dI}{dt}\). Its S.I. unit is the henry (H).

(ii) Mutual inductance: When a current \(I_1\) in one coil produces a flux linkage \(N_2\Phi_2 = M I_1\) in a neighbouring coil, \(M\) is the mutual inductance. It is the e.m.f. induced in the secondary coil per unit rate of change of current in the primary coil: \(e_2 = -M\dfrac{dI_1}{dt}\). S.I. unit: henry (H).

Numerical: \(A = 1\) m\(^2\), \(B_1 = 3\) Wb/m\(^2\), \(B_2 = 1\) Wb/m\(^2\), \(dt = 0.5\) s, loop normal to the field (\(\theta = 0\)).

The induced e.m.f. is 4 V; by Lenz’s law it drives a current that tries to keep the flux from decreasing.