Q. Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of length l and mass m is given velocity v_{0} as shown. The whole system is placed in perpendicular magnetic field B. Find the maximum current in the inductor. (neglect gravity and friction)

(a) $ \displaystyle \frac{m v_0}{L}$

(b) $ \displaystyle \sqrt{\frac{m }{L}} v_0 $

(c) $ \displaystyle \frac{m v_0^2}{L}$

(d) None of these

Ans: (b)

Sol: $ \displaystyle \frac{1}{2}L I_0^2 = \frac{1}{2} m v_0^2 $

$ \displaystyle L I_0^2 = m v_0^2 $

$ \displaystyle I_0^2 = \frac{m}{L} v_0^2 $

$ \displaystyle I_0 = \sqrt{\frac{m }{L}} v_0 $