Question

A semicircular wire of radius $R$ is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength $B$. The induced emf between the ends is

• A. $B\omega R^2/2$
• B. $2B\omega R^2$
• C. is variable
• D. none of these

Answer 1

The correct option is B $2B\omega R^2$

Induced motional emf in $MNQ$ is equivalent to the motional emf in an imaginary wire $MQ$.

Therefore,

$e_{MNQ}=e_{MQ}$
$=\frac{1}{2}{B\omega l}^2$
$={2B\omega R}^2(\because l=2R)$