Question

A small ball of volume `V` made of paramagnetic with susceptibility `chi` was slowly displace along the axis of a current-carrying coil from the point where the magnetic induction equals `B` out to the region where the magnetic field is the practically absent. What amount of work was performed during this process ?

Answer 1

`F_(x) = (vec(p_(m)) . vec(grad)) B_(x) = (chi B V)/(mum mu_(0)) (dB)/(dx) = (chi V)/(2 mu_(0)) (dB^(2))/(dx)`
This force is attractive and an equal force must be applied for balance. The weok done by applied forces is,
`A = int_(x = 0)^(x = L) -F_(x) dx = (chi V)/(2 mu_(0)) (-B^(2))_(x = 0)^(x = L) = (chi V B^(2))/(2 mu_(0))`