Question

A wire is bent to form a semicircle of radius $a$ . The wire rotates about its one end with angular velocity $\omega $ . Axis of rotation being perpendicular to the plane of the semicircle. In the space, a uniform magnetic field of induction $B$ exists along the axis of rotation, as shown in figure. Then

• A. potential difference between $P$ and $Q$ is equal to $2B\omega a^{2}$
• B. potential difference between $P$ and $Q$ is equal to $2\pi ^{2}B\omega a^{2}$
• C. $P$ is at higher potential than $Q$
• D. none of these

Answer 1

Answer: (A)

$e=\frac{1}{2}B\omega l^{2}$
$e=\frac{1}{2}B\omega \left(2 a\right)^{2}$
$e \, = \, 2B\omega a^{2}$