Problem 3.295

A metal rod of mass $m$ can rotate about a horizontal axis O, sliding along a circular conductor of radius a (Fig. 3.83). The arrangement is located in a uniform magnetic field of induction $B$ directed perpendicular to the ring plane. The axis and the ring are connected to an emf source to form a circuit of resistance $R .$ Neglecting the friction, circuit inductance, and ring resistance, find the law according to which the source emf must vary to make the rod rotate with a constant angular velocity $\omega$.