# Electrostatic potential energy for concentric spheres

1. Mar 16, 2007

### wombat7373

Two concentric metal spheres have radii $$r_1$$ = 10 cm and $$r_2$$ = 10.5 cm. The inner sphere has a charge of Q = 5 nC spread uniformly on its surface, and the outer sphere has charge -Q on its surface. (a) calculate the total energy stored in the electric field inside the spheres Hint: You can treat the spheres essentially as parallel flat slabs separated by 0.5 cm why?

$$\phi = 4\pi kQ$$
U=qV/2

First of all, I don't know why treating the spheres as slabs will help, but since that's the hint, I'm looking for a way to do it. I can show with Gauss' Law that teh electric field inside the inner sphere is 0, so that kind of makes them like slabs. Is that enough justification and why?

Last edited: Mar 16, 2007
2. Mar 16, 2007

### G01

HINT: Think capacitors. How do you find the energy stored in a capacitor?

Two charged slabs separated by some distance d, is essentially a capacitor.
This is why treating the spheres as flat surfaces will help. The curvature will not really affect the situation, it is essentially a capacitor, whether spherical or flat.

3. Mar 16, 2007

### wombat7373

I suppose I'll buy it just because the electric field ends up being constant like with two plates. So to find the energy I just do U=(1/2)QV. I suppose I could calculate the potential difference by integrating the electric field over that 0.5 cm distance. Would that be the way to do it?

4. Mar 16, 2007

### G01

I think its safe to assume that the field is constant within the capacitor. You shouldn't have to integrate, unless you want the practice of course

I would go about this using the formula for energy stored in an electric field, which is:

$$U = 1/2 C V^2$$

Last edited: Mar 16, 2007