Question

An infinitely long cylinderical wire of radius R is carrying a current with current density `j=alphar^(3)` (where `alpha` is constant and r is the distance from the axis of the wire). If the magnetic fixed at `r=(R)/(2)` is `B_(1)` and at r=2R is `B_(2)` then the ratio `(B_(2))/(B_(1))` is
A. 2
B. 4
C. 6
D. 8

Answer 1

Correct Answer - D

When `rleR`
`B2pir=mu_(0)underset(0)overset(r)intj2pirdr`
`Br=(mu_(0)alphar^(5))/(5)`
`B=(mu_(0)alphar^(4))/(5),rleR`
when `r gt R`
`B2pir=mu_(0)underset(0)overset(R)intj2pirdr`
`Br=mu_(0)underset(0)overset(R)intalphar^(3)rdr`
`Br=(mu_(0)alphaR^(5))/(5)`
`thereforeB=(mu_(0)alphaR^(5))/(5r),rgtR`
at `r=(R)/(2),B_(1)=(mu_(0)alphaR^(4))/(80)`
at `r=2R,B_(2)=(mu_(0)alphaR^(4))/(10)`
`therefore(B_(2))/(B_(1))=8`