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The potential in the electric field vari...

The potential in the electric field varies as `V = -a x^2 + b` with respect to x - coordinate, where a and b are constants. Find the charge density `rho (x)` in a space.

A

`-6_aepsilon_0r`

B

`-24 pi_a epsilon_0`

C

`-6_a epsilon_0`

D

`-24 pia epsilon_0 r`

Text Solution

Verified by Experts

The correct Answer is:
C
Electric field `E=- (d phi)/(dr)=-2ar`
By Gauss theorem `E(4 pi r^2)=q/e_0 implies q=-8pie_0 ar^3`
`p=(dq)/(dV)=(dq)/(dr) times (dr)/(dV)=(-24 pi e_0 ar^2) (1/(4 pi r^2))=-6 e_0 a`
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