# Electrostatic potential inside/outside sphere

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1. Oct 10, 2015

### j3dwards

1. The problem statement, all variables and given/known data
A sphere of radius R carries an electric charge Q, uniformly distributed inside its volume.

(a) Using the expression for the electric field given in the lectures, compute the electrostatic potential V (r) inside and outside the sphere.

2. Relevant equations
E
= -V

3. The attempt at a solution
E
= Qr/4πεoR3 = -V

VE= - ∫c E . dl

But now I'm really unsure of how you get V from this? Because you can't divide by the gradient function... So do I integrate E = Qr/4πεoR3 to find V?

Last edited: Oct 10, 2015
2. Oct 10, 2015

### blue_leaf77

You also need the expression of the field outside the sphere.
Correct, except for the "C" subscript after the integral, you will not be integrating in a closed loop, instead use the radial property of the field to find V from its gradient.