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 $