A rod of length l is rotating at a uniform angular velocity about its perpendicular bisector. A uniform magnetic field B is present parallel to the rotation axis. The potential difference between the two ends of the rod is

Step-by-step solution

Let the center of the rod be O and its two ends be A and B . The rod rotates about its perpendicular bisector, so the distance of both ends from the axis of rotation is l/2 . The motional emf induced between the center O and end A is given by: V_A - V_O = 1 2 B ( l 2 )^2 = 1 8 B l^2 Similarly, the motional emf induced between the center O and end B is: V_B - V_O = 1 2 B ( l 2 )^2 = 1 8 B l^2 The potential difference between the two ends A and B is: V_A - V_B = (V_A - V_O) - (V_B - V_O) = 0 Alternatively, the induce