Find the current density as a funciton of distance `r` from the axis of a radially symmetrical parallel stream of electrons if the magentic induction inside the strems varies as `B = br^(2)`, wheree `b and `alpha` are positive contans.

Explanation

By Circulation theorem
`B_(varphi) 2pi r = mu_(0) int_(0)^(r) j (r') xx2pi r' dr'`
or using `B_(varphi) = br^(a)` inside the streram,
`br^(alpha + 1) = mu_(0) int_(0)^(r) j (r') r' dr'`
So by differenctiation,
`(alpha + 1) bt^(alpha) = mu_(0) j(r) r`
Hence, `j(r) = (b(alpha + 1))/(mu_(0)) r^(alpha - 1)`