Electrostatic potential inside/outside sphere

[j3dwards]

Homework Statement

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.

Homework Equations

E[/B] = -∇V

The Attempt at a Solution

E[/B] = Qr/4πε_oR³ = -∇V

V_E= - ∫_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/4πε_oR³ to find V?

 

[blue_leaf77]

You also need the expression of the field outside the sphere.

VE= - ∫c E . dl

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.