A coil has an area $0.06 \mathrm{~m}^2$ and it has 600 turns. After placing the coil in a magnetic field of…
A coil has an area $0.06 \mathrm{~m}^2$ and it has 600 turns. After placing the coil in a magnetic field of strength $5 \times 10^{-5} \mathrm{Wbm}^{-2}$, it is rotated through $90^{\circ}$ in 0.2 second. The magnitude of average e.m.f induced in the coil is
$12 \times 10^{-3} \mathrm{~V}$
$3 \mathrm{mV}$
$3 \mathrm{~V}$
$9 \times 10^{-3} \mathrm{~V}$
Solution
Induced emf, $\mathrm{e}=\frac{-\mathrm{N}\left(\phi_2-\phi_1\right)}{\mathrm{t}}=\frac{-\mathrm{NBA}\left(\cos \theta_2-\cos \theta_1\right)}{\mathrm{t}}$
Assuming that the coil was initially placed perpendicular magnetic flux
$\begin{aligned}
& \theta_1=0^{\circ} \text { and } \theta_2=90^{\circ} . \\
& \mathrm{e}=\frac{-\mathrm{NBA}\left(\cos 90^{\circ}-\cos 0^{\circ}\right)}{\mathrm{t}} \\
& =\frac{-\mathrm{NBA}(0-1)}{\mathrm{t}}=\frac{\mathrm{NBA}}{\mathrm{t}} \\
& =\frac{600 \times 5 \times 10^{-5} \times 0.06}{0.2}=9 \times 10^{-3} \mathrm{~V}
\end{aligned}$