Question

Figure shows a conducting circular loop of radius $a$ placed in a uniform, perpendicular magnetic field $B$. A thick metal rod $OA$ is pivoted at the centre $O$. The other end fo the rod touches the loop at $A$. The centre $O$ and a fixed point $C$ on the loop are connected by a wire $OC$ of resistance $R$. A force is applied at the middle point of the rod $OA$ perpendicularly so that the rod rotates clockwise at a uniform angular-velocity $\omega$. Find the force.

Answer 1

$e=Bvl=\frac{B\times a\times \omega \times a}{2}$
$i=\frac{B{a}^2\omega }{2R}$
$F=ilB=\frac{B{a}^2\omega }{2R}\times a\times B=\frac{B^2{a}^3\omega }{2R}$