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Consider a long cylindrical wire carryin...

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).

Text Solution

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The correct Answer is:
3
`int bar(B).bar(dl)=u_(0)i_("ene")`
`implies B(2pir)=mu_(0)int_(0)^(R) 2pirdr=mu_(0)int_(0)^(r)2piCr^(n-1)dr`
`kr^(4)xx2pir=mu_(0)2piC (r^(n+2))/(n+2)impliesn+2=5impliesn=3`
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