Q 12-06-069JEE MainJEE Main 2023 (24 Jan, Shift 2)Easy
A metallic rod of length $L$ is rotated with an angular speed of $\omega$ normal to a uniform magnetic field $B$ about an axis passing through one end of rod as shown in figure. The induced emf will be
Answer: (C) $\dfrac12BL^2\omega$
An element $dr$ at distance $r$ moves with speed $\omega r$: $d\varepsilon=B\omega r\,dr$.
$$\varepsilon=\int_0^LB\omega r\,dr=\frac12B\omega L^2$$
Solution by Sreeraj P, M.Sc Physics