A cylindrical conductor of radius R carries a current along its length. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to J = br, where b is a constant. Find an expression for the magnetic field B.

(a) at `r_1 lt R`
(b) at distance `r_2 gt R`, measured from the axis.
Hint [use Ampere's Law]

Explanation

`B_(1) = (mu_0 br_(1)^(2))/(3). B_(2) = (mu_0 R^3)/(3r_2)`