5. The lower end of the thin uniform rod in is attached to the floor by a frictionless hinge at point P. The rod has mass m and length L and is in a uniform magnetic field B that is directed into the page. The rod finds an equilibrium position due to the force exerted by a horizontal spring (with a spring constant k) that connects the top of the rod to the wall. The spring extension was zero before the current I was switched on and then it is extended to a distance of d after the current was on. The current I is in the direction toward P. Find the equilibrium angle q.
(hint: Find the torques due to the magnetic force, weight and the force due to the spring. Take the axis point at P. You can take the weight acting at the center of the rod. Think about how you are going to calculate the torque due to the magnetic force. Can you use an integration? If not use an approximation).