Electric potential?

please solve it in detail?enter image source here

1 Answer
Sep 11, 2017

(B)

Explanation:

We know that electric potential V is related to space charge density rho through Poisson's equation

gradcdot grad V=(-rho)/epsilon_0
=>grad^2V=(-rho)/epsilon_0
where epsilon_0 is permittivity.

It is given that the potential function is dependent on x-coordinate only. Therefore, we get

rho=-epsilon_0(d^2V)/dx^2

Inserting given function of V we have

rho=-epsilon_0(d^2)/dx^2(-2x^3+3)
=>rho=epsilon_0(d)/dx(6x^2)
=>rho=12epsilon_0 x

.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-

The electric field vecE is related to the charge density rho through the divergence relationship

grad cdot vecE=rho/epsilon_0

and the electric field is related to the electric potential V by a gradient relationship

vecE=-gradV

Combining these two we get Poisson's equation