Question

A coil has 1000 turns and $500\, cm ^{2}$ as its area. The plane of the coil is placed perpendicular to a uniform magnetic field of $2 \times 10^{-5} T$. The coil is rotated through $180^{\circ}$ in $0.2$ seconds. The average emf induced in the coil, in $mV$ is

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

Answer: (B)

When the plane of a coil is perpendicular to the field, the flux linked with the coil is
$\phi_{1}=N B A \cos 0^{\circ}=N B A$
When the coil is turned through $180^{\circ}$, the flux linked with the coil is
$\phi_{2}=N B A \cos 180^{\circ}=-N B A$
$\left(\because \cos 180^{\circ}=-1\right)$
$\therefore $ Change in flux, $\Delta \phi=\phi_{2}-\phi_{1}$
$=-N B A-N B A=-2 N B A $
$|\Delta \phi|=2 N B A$
Magnitude of average emf induced is
$\left|\varepsilon_{ av }\right|=\frac{|\Delta \phi|}{\Delta t}=\frac{2 N B A}{\Delta t}=\frac{2 \times 1000 \times 2 \times 10^{-5} \times 500 \times 10^{-4}}{0.2}$
$=10 \times 10^{-3} V =10\, mV$