As shown in the figure, suppose the wire connecting O and C has zero resistance while the circular loop possesses a resistance R uniformly distributed along its length. The rod OA is made to rotate with a uniform angular speed . Determine the current in the rod when AOC = 90^ .

Step-by-step solution

The motional emf e induced in the rotating rod OA is given by e = 1 2 B a^2 . The circular loop has a total resistance R uniformly distributed along its length. When AOC = 90^ , the points A and C divide the loop into two arcs: a minor arc of angle 90^ and a major arc of angle 270^ . The resistance of the minor arc is R₁ = 90^ 360^ R = R 4 . The resistance of the major arc is R₂ = 270^ 360^ R = 3R 4 . Since the current from the rod at A can flow to C through either arc, these two arcs are in parallel between A and