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.

Answer

(a) `b_(z)=(mu_(0))/(4pir^(3))[2 cos^(2) theta -sin^(2)theta]`
(b) `phi=(mu_(0)MR^(2))/(2(R^(2)+z^(2))^(3//2))`
(c) `E_("in")=(3mu_(0)MR^(2)vz)/(2(R^(2)+z^(2))^(5//2))`