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. `(81pia^(2)R^(4))/(144)`

Answer

A

Explanation

Current density `J=ar^(2)`
Current `I=intJ.dA=underset(R//3)overset(R//2)intar^(2)(2pirdr)" "["where "dA=2pirdr]`
`=2pia[(r^(4))/(4)]_(R//3)^(R//2)=(65piaR^(4))/(2592)`