Question

In the figure there are two identical conducting rods each of length ${}^{\prime }{a}^{\prime }$ rotating with angular speed $\omega$ in the directions shown. One end of each rod touches a conducting ring. Magnetic field $B$ exists perpendicular to the plane of the rings. The rods, the conducting rings and the lead wires are resistanceless. Find the magnitude and direction of current in the resistance $R$.

Answer 1

emf induced in each loop is $\left|e\right|$

$e=\frac{1}{2}\omega Ba$

Total emf in the circuit is,

$2e=\omega Ba$

Current $i=\frac{2e}{R}=\frac{\omega Ba}{R}$ direction shown in fig