A rectangular coil of single turn, having area A, rotates in a un… - Vidyadip

MCQ

$A$ rectangular coil of single turn, having area $A$, rotates in a uniform magnetic field $B$ an angular velocity $\omega$ about an axis perpendicular to the field. If initially the plane of coil is perpendicular to the field, then the average induced $e.m.f.$ when it has rotated through $90^o$ is

A
$\frac{{\omega BA}}{\pi }$
B
$\frac{{\omega BA}}{{2\pi }}$
C
$\frac{{\omega BA}}{{4\pi }}$
✓
$\frac{{2\omega BA}}{\pi }$

✓

Answer

Correct option: D.

$\frac{{2\omega BA}}{\pi }$

d
Initially flux, $\phi=B A \cos 0=B A$

After rotating through an angle $90^{\circ} .$

Flux through the coil is zero.

So, $\Delta \phi=B A$

Angular speed $=w,$ so, time period $=\frac{2 \pi}{\omega}=T$

$\frac{T}{4}$ is time taken to rotate $90^{\circ}$

So, $\frac{\Delta \phi}{\Delta t}=\frac{B A}{T / 4}=\frac{2 B A \omega}{\pi}$

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