Problem 3.298

A wire shaped as a semi-circle of radius $a$ rotates about an axis $O O^{\prime}$ with an angular velocity $\omega$ in a uniform magnetic field of induction $B$ (Fig. 3.85). The rotation axis is perpendicular to the field direction. The total resistance of the circuit is equal to $R$. Neglecting the magnetic field of the induced current, find the mean amount of thermal power being generated in the loop during a rotation period.