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The electrostatic potential inside a cha...

The electrostatic potential inside a charged spherical ball is given by `phi=ar^2+b` where r is the distance from the centre and a, b are constants. Then the charge density inside the ball is:

A

`-24piaepsilon_(0)r`

B

`-6aepsilon_(0)r`

C

`-24piaepsilon_(0)`

D

`-6aepsilon_(0)`

Text Solution

Verified by Experts

The correct Answer is:
D
`phi=ar^(2)+b`
`E=-(d phi)/(dt)=-2ar`
`ointvecE.dvecS=(q)/(epsilon_(0))implies-2arxx4pir^(2)=(q)/(epsilon_(0))`
`implies q=-8epsilon_(0)apir^(3)`
`rho=(q)/((4)/(3)pir^(3))impliesrho=-6aepsilon_(0)`.
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