# Electricity and Magnetism (Charged Plates)

1. Nov 12, 2009

### Mathsboi

First year studying Physics at university.
I've got my first E&M assignment and it's about charged plates but the thing is, I'm certain we haven't covered most of what it is asking, and I can hardly find any (simple) explanations to what I'm meant to do or methods I'm meant to use.

I wasn't sure weather to put it here, or in homework, so if I'm wrong, sorry :( (Reason being that I don't really want specific help with the homework but more about the topic itself).

It is relatively straight forward (I think, unless it's more complex than I'm thinking).
It says two metal plates of a thickness (let's just say $$l_a$$ for length of plates) separated by a distance $$z$$ with a P.D of $$V$$. Ignoring edge effects calculate the charges and electric fields within the system. Plot a graph of charge density against position across the back of one plate to the back of the other. Hence draw a graph of electric field against position over the same range.

So here's what I attempted/need explaining to me (please tell me if I'm wrong anywhere):

To calculate the Electric field I would use this:
$$E=\frac{V}{d}$$ where $$d=z$$.

In this case the plates would be infinite, no? So it would be charge density (charge per unit squared) instead of just plain charges.
So to work out the charge density $$\sigma$$ I'd use
$$E=\frac{|\sigma|}{2\epsilon_0}$$ - I'm not convinced about this though, why would it be over $$2\epsilon_0$$ ?

Also if E is calculated from above, how does with work with
$$\nabla\cdot E = \frac{\sigma}{\epsilon_0}$$
because surely that would mean that E = 0 if you partially differentiated it?

As for the graphs they would look like this, no?
(axes: both x are position, y1 is charge density with max at sigma and minimum at -sigma at positions labeled and y2 is electric field with maximum at E)

I understand the graphs, but obviously not fully (I know why it becomes a box from the straight lines) - because I can't explain it! Why does charge only appear at the surface and not inside the plate itself?

Would someone be able to help explain the theory behind this please? Then I can ask about question (ii)