State Faraday’s law for electromagnetic induction.
A long solenoid has a cross-section diameter of $3.2\,\text{cm}$. A coil $C$, with $85$ turns of wire, is wound tightly around the central region of the solenoid. The magnetic flux density $B$, in tesla, at the centre of the solenoid is given by $B = \pi \times 10^{-3} \times I$, where $I$ is the current in the solenoid in ampere. Show that, when the current $I$ is $2.8\,\text{A}$ in the solenoid, the magnetic flux linkage of coil $C$ is $6.0 \times 10^{-4}\,\text{Wb}$.
The current $I$ in the solenoid in (b) is reversed over $0.30\,\text{s}$. Calculate the mean e.m.f. induced in coil $C$.
The current $I$ in the solenoid in (b) is now changed 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 $t$.