Question #42974

A small square conducting loop of mass $m$ (in kg), side length $a$ (in m), and electrical resistance $R$ (in $\Omega$) is attached to the lower end of a massless rigid rod of length $L$ (in m). The upper end of the rod is pivoted so the loop can oscillate as a pendulum in the vertical $xy$-plane ($x$ is horizontal, $y$ is vertical). A time-independent magnetic field $\vec{B} = (B_0 + \alpha x) \hat{k}$ (in T) exists in the region, where $B_0$ and $\alpha$ are positive constants. An external horizontal driving force $F(t) = F_0 \cos(\omega t)$ (in N) is applied to the loop. Assuming small amplitude oscillations, negligible self-inductance, and no air drag, what is the average electrical power (in W) dissipated in the loop when the system is driven at its velocity resonance frequency?