A straight metallic rod of total length 1.5 m is pivoted at a point 0.5 m from one of its ends. It is rotated with a constant angular velocity of 10 rad/s in a uniform magnetic field of 4.0 T which is perpendicular to the plane of rotation. The potential difference between the two extreme ends of the rod is

Step-by-step solution

Let the pivot point be O . The rod is divided into two segments of lengths r₁ = 1.0 m and r₂ = 0.5 m on opposite sides of the pivot. The motional EMF induced across a rotating rod of length r is given by = 1 2 B r^2 . For the longer segment: ₁ = 1 2 4.0 10 (1.0)^2 = 20 V For the shorter segment: ₂ = 1 2 4.0 10 (0.5)^2 = 5 V Since the two segments are on opposite sides of the pivot and rotate in the same sense, the velocity vectors of points on the two segments are in opposite directions. By Fleming's right-hand rul