As shown in the figure, a conducting circular loop of radius a is situated in a uniform, perpendicular magnetic field B . A thick metal rod OA is pivoted at the centre O , and its other end touches the loop at A . A wire OC with resistance R connects the centre O to a fixed point C on the loop. A force is applied perpendicularly at the midpoint of the rod OA , causing the rod to rotate clockwise at a uniform angular

Step-by-step solution

The motional emf induced in the rotating rod OA of length a is given by: = 1 2 B a^2 Since the circular loop is conducting, the rod OA and the wire OC form a closed electrical circuit with resistance R . The induced current I flowing through this circuit is: I = R = B a^2 2R The magnetic force on a small element dx of the rod at a distance x from the center O is dF_m = I B dx . The total magnetic torque _m opposing the rotation about O is: _m = ₀^a x dF_m = ₀^a I B x dx = 1 2 I B a^2 The external force F is applied