Question

A wire loop enclosing a semicircle of radius $R$ is located on the boundary of uniform magnetic field $B$. At time $t=0$, the loop is set into motion with constant angular accleration $\alpha$ about an axis passing through $O$ and is perpendicular to semicircle. The clockwise emf direction is taken to be positive. The modulus of variation of emf as a function of time is ($0<\theta <\pi$),
then the variation of emf as a function of time is given by the graph

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

For ($0<\pi$), $ϵ=-\frac{B{R}^2\alpha t}{2}$
For ($0<2\pi$),
$\varphi =B\frac{(2\pi -\theta )R^2}{2}$
$ϵ=-\frac{d\varphi }{dt}=\frac{B{R}^2\alpha t}{2}$