Question #43881

A rectangular conducting loop of mass $m = 1 \text{ kg}$, resistance $R = 10 \text{ } \Omega$, and width $L = 2 \text{ m}$ is connected to a fixed support by a massless spring of spring constant $k = 200 \text{ N/m}$. The loop is partially placed in a uniform magnetic field $B = 5 \text{ T}$ directed perpendicular to the plane of the loop. An external driving force $F(t) = 20\sqrt{2} \cos(10t) \text{ N}$ is applied to the loop in its plane, perpendicular to the magnetic field boundary. Assuming the loop never fully enters or exits the magnetic field region, find the phase angle $\phi$ by which the applied force $F(t)$ leads the displacement $x(t)$ of the loop, and the average power $P$ dissipated in the resistor in the steady state.