# Energy stored in electric field

1. Oct 13, 2011

### Fluorescent

1. The problem statement, all variables and given/known data
It's told me to treat two charged concentric sphere's as parallel plates with Q=5nC on one, and -Q on the other (both with uniform spread). The distance between them is 5mm, and the surface area of each plate/sphere is 0.13m2. Calculate the energy stored in the electric field between the plates?

2. Relevant equations
Obviously, parallel plates can use the equation E=Vd because there's an uniform electric field, but I don't know E or V so that equation is as good as useless. Do you think it expects me to manipulate capacitance equations to work out the answer?

Because they are infact charged sphere's, can I use equations which use the inverse square law in them? Or do i have to stick to the fact they are now parallel plates?
3. The attempt at a solution
So there's a uniform electric field, but I don't really understand what it means by energy within the electric field?

The following question is asking me to work out the total energy stored if this setup were a capacitor (which is easy enough, using Q=CV etc.), but not sure what equations to use if were looking at a normal uniform electric fields question?

Last edited: Oct 13, 2011
2. Oct 13, 2011

### Staff: Mentor

The parallel plate capacitor interpretation of a spherical capacitor can be fairly accurate for certain arrangements of the geometry. In this case you're told to use the approximation, so be fearless! Calculate the capacitance as though the given area was the area of the rectangular plates, and 5mm is the separation.

With the capacitance calculated and given the charge on the cap, you can work out the voltage or energy just as you would normally.

3. Oct 13, 2011

### Fluorescent

Are you sure there's not a second way of doing it because in the second part of the question it asks me to "compute the total energy stored in the capacitor". If I did it your way, surely I'd be doing the same thing for part i) and ii).

Although from the outset it's clear where the question is heading, it doesn't actually say capacitor at any point in part i), just "calculate the total energy stored in the electric field". It also mentions Energy Density of electric fields further up the question if that helps...

4. Oct 13, 2011

### Staff: Mentor

Without seeing the entire question to put things in context I can't tell what their intent was for solution methods.

EDIT: One idea occurs to me. If you were to use the given charge and plate area to determine the charge density on each plate then you could, by assuming a uniform field between them, use the formula for the field produced by a uniform sheet of charge to determine the field strength between the plates. Then the energy density will be given by the volume integral (over the volume between the plates):

$$U = \int_V \frac{1}{2}\epsilon_o |E|^2 dV$$

Last edited: Oct 13, 2011