The current density varies radical distance r as `J=ar^(2)`, in a cylindrical wire of radius R. The current passing through the wire between radical distance `R//3 and R//2` is,

Options

A. `(65piaR^(4))/(2592)`
B. `(25piaR^(4))/(72)`
C. `(65pia^(2)R^(3))/(2938)`
D. None of these

Answer

A

Explanation

Given , `J=ar^(2)`
`i=underset(1)overset(2)intJxx2pirdr=underset(R//3)overset(R//2)intar^(2)2pirdr`
`2piaunderset(R//3)overset(R//2)intr^(3)dr=2pia|(r^(4))/(4)|_(R//3)^(R//2)`
`=(pia)/(2)[((R)/(2))^(4)-((R)/(3))^(4)]`