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The current density varies radical dista...

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,

A

`(65piaR^(4))/(2592)`

B

`(25piaR^(4))/(72)`

C

`(65pia^(2)R^(3))/(2938)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Current density `J=ar^(2)`
Current `l=int JdA`
`l=underset(R//3)overset(R//2)(int)ar^(2)(2pirdr), ("where" dA=2pirdr)`
`=2pia[(r^(4))/(4)]_(R//3)^(R//2)=(65piaR^(4))/(2592)`
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