State Faraday’s law governing electromagnetic induction.
The cross-section of a long solenoid has diameter $3.2\,\text{cm}$, as shown in Fig. 9.1. Coil C, which has 85 turns of wire, is wound tightly around the central part of the solenoid. The magnetic flux density $B$, in tesla, at the centre of the solenoid is given by $B = \pi \times 10^{-3} I$, where $I$ is the current in the solenoid in ampere. Show that, when the current $I$ is $2.8\,\text{A}$, the magnetic flux linkage of coil C is $6.0 \times 10^{-4}\,\text{Wb}$.
In (b), the current $I$ in the solenoid is reversed in $0.30\,\text{s}$. Calculate the mean e.m.f. induced in coil C.
The current $I$ in the solenoid in (b) is now varied with time $t$ as shown in Fig. 9.2. Use your answer to (c) to show, on Fig. 9.3, how the e.m.f. $E$ induced in coil C varies with time $t$.