A conducting rod of length L is free to rotate in a horizontal plane about one of its ends. The rod is initially at rest and begins to rotate with a constant angular acceleration α about its pivot. A uniform vertical magnetic field of magnitude B is present in the space. The resistance between the ends of the rod is R and the rod maintains good electrical contact throughout its motion.
(i) Derive an expression for the emf induced between the centre of rotation and the free end of the rod as a function of time for t≥0.
(ii) Find the expression for the instantaneous induced current as a function of time and specify its direction.
(iii) Determine the total electrical energy dissipated in the resistance during the first t seconds of motion.