Q. A semicircular wire of radius R is rotated with constant angular velocity ω 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) BωR²/2

(b) 2BωR²

(c) is variable

(d) none of these

Ans: (b)

Sol: Induced emf between end points of semicircular wire is

$ \displaystyle e = \frac{1}{2}B\omega l^2 $

Here , l = 2R

$\displaystyle e = \frac{1}{2}B\omega (2R)^2 $

$ \displaystyle e = 2 B \omega R^2 $