ODBAC is a fixed rectangular conductor of negligible resistance (co is not connected) and OP is a conductor which rotates clockwise with an angular velocity $w$ as shown in the fig. The entire system is in a uniform magnetic field B whose direction is along the normal to the surface of the rectangular conductor ABDC. The conductor OP is in electric contact with ABDC. The rotating conductor has resistance of X per unit length. Find the current in the rotating conductor as it rotates by $180^{\circ}$

Question

$(a)\;\frac{Blw}{ \lambda \sin wt}$
$(b)\;\frac{Blw}{2 \sin wt}$
$(c)\;\frac{Blw}{2 \lambda \sin wt}$
$(d)\;\frac{Blw}{ \sin wt}$