Consider a long cylindrical wire carrying current along the axis of wire. The current distributed non-uniformly on cross section. The magnetic field B inside the wire varies with distance `r` from the axis as `B=kr^(4)` where k is a cosntant. The current density `J` varies with distance `r` as `J=cr^(n)` then the value of `n` is (where c is another constant).

Answer

3

Explanation

`intvecB.overline(dl)=u_(0)i_(ene)`
`impliesB(2pir)=mu_(0)int_(0)^(r)j2pirdr=mu_(0)int_(0)^(r)2piCr^(n+1)dr`
`implieskr^(4)xx2pir=mu_(0)2piC(r^(n+2))/(n+2)impliesn+2=5impliesn=3`