A short bar magnet having magnetic dipole moment M is moving along the axis of a fixed conducting (non magnetic) ring of radius R. The axis of the ring is along z direction.

(a) Write the z component of magnetic field due to the magnetic dipole at a point P in the plane of the ring, at the instant the magnet is at a distance z from the centre of the ring. Position of point P can be defined in terms of angle `theta` as shown.
(b) Write the magnetic flux through the ring due to the magnetic field produced by the magnet as a function of z.
(c) Write the magnitude of emf induced in the ring at the instant shown if speed of the magnet at the moment is v.