In the middle of a long solenoid there is a coaxial ring of square cross-seciton, made of conducting materaial with respectivity are equal to `h` its inside and outside radii are equal to `a` and `b` respectively. Find the current induced in the ring if the magnetic induction produced by the solenoid varies with time as `B = beta t`, where `beta t`, where `beta` is constant. THe inductance of the ring is to be neglected.

Explanation

Take an elementary ring of radius `r` and width `dt`. The e.m.f induced in this elementary ring is `pi r^(2) beta`.
Now the conductance of this ring is.
`d ((1)/(R)) = (h dr)/(rho 2 pi r)` so `d I = (h r dr)/(2 rho) beta`
Intergating we get the total current,
`I = int_(a)^(b) (hr dr)/(2 rho) beta = (h beta (b^(2) - a^(2)))/(4 rho)`