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

1

Explanation

Current density `J=ar^(2)`
C urrent `I=int jdA`
`I=int_(R//3)^( R//2) ar^(2)(2pi rdr)` [where dA ` 2pirdr`)
`=2pia[(r^(4))/(4)]_(R//3)^(R//2)=(65piaR^(4))/(25892)`