# Homework Help: Gauss' Law between infinite plates

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1. May 12, 2016

### flintbox

1. The problem statement, all variables and given/known data
The volume between two infinite plates located at x=L and x=-L respectively is filled with a uniform charge density $\rho$. Calculate the electric field in the regions above, between and below the plates. Calculate the potential difference between the points x=-L and x=L.

2. Relevant equations & attempt
I want to apply Gauss' Law, but I don't know how to. To me it seems that inside the plates, the charge enclosed is that of any surface, but I wouldn't know the flux of the electric field. I tried searching literature, but they all consider charged plates, whereas here, the plates are just boundaries.

Last edited by a moderator: May 12, 2016
2. May 12, 2016

### Staff: Mentor

Hint: Take advantage of symmetry. Imagine a Gaussian surface in the shape of a cube centered at x = 0.

3. May 12, 2016

### flintbox

But I am confused about the direction of the electric field inside the plates, since there is a charge density everywhere.

4. May 12, 2016

### nrqed

Other hint: consider any point exactly midway between the two plates, what can you say about the E field there?

Now, consider another point between the two plates but not exactly midway this time. You should be able to tell what the direction of the E field is, there. Using only the symmetry of the problem (consider the plates to be infinite).

5. May 12, 2016

### Staff: Mentor

Take $\rho$ as positive. All that matters in the charge within your Gaussian surface. If the charge enclosed is positive, which way must the field point?

6. May 12, 2016

### flintbox

The E field just above the center points upward and the E field below downwards. Thank you! I think I can do it now.

7. May 12, 2016

### flintbox

Then the field points outwards! Thanks

8. May 12, 2016

### rude man

Careful with the Gaussian surfaces! In addition to the volume charges there are also induced surface charges!

(This problem is also easily solved by solving Poisson's equation.)

9. May 12, 2016

### flintbox

I've used Gauss to determine the Electric field inside to be $2\pi \rho x$ (CGS units), but what about outside? I don't know how to apply Gauss since there is no charge enclosed.

Last edited by a moderator: May 12, 2016
10. May 12, 2016

### Staff: Mentor

If a Gaussian surface extends beyond the plates, then it encloses the charge between them.

11. May 12, 2016

### rude man

I can't read your post and I'd have to convert to SI.
Run a surface from inside one of the plates to any outside region. Remember what I said about surface charges ...

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