# Homework Help: 2 Charged thick plates placed next to each other.

1. Feb 14, 2013

### Ghastn

1. The problem statement, all variables and given/known data

Two thick, parallel plates of thickness d and uniform charge densities
(Coulombs per unit volume) ρ and −ρ are placed next to each other, as
shown in the figure. The negatively charged plate is located between –d
and 0 on the x-axis and the positively charged plate between 0 and d on
the x-axis. The z-axis points out of the page. Assume that both plates
are infinite in y and z. Find the expressions for the x-, y-, and zcomponents
of the electric field E(x) as a function of the x-coordinate.
Write your solution in terms of ε0, not ke.
Is the net force per unit area between the plates: attractive, repulsive or zero.
Setup the integral to compute the pressure on the plates

2. Relevant equations

I believe Gauss Law could be used: Flux = Qin/ε.

3. The attempt at a solution
I would imagine a cylinder crossing the 2 plates and measure the field on each surface: they are going to be in the same direction, I think. The problem is that I cannot fully imagine the situation: Is the field w on the left and equal to the sum on the right?

2. Feb 14, 2013

### haruspex

3. Feb 14, 2013

### Ghastn

I don't think that would work as we are not looking at the interaction between the two plates but rather the superposition of the two fields: Here is the image:
http://img163.imageshack.us/img163/5497/phys.jpg [Broken]
Any guesses?

Last edited by a moderator: May 6, 2017
4. Feb 14, 2013

### haruspex

I'm suggesting that you can divide each think plate into a stack of parallel thin plates. The field at some point within a thick plate then translates to the field between thin plates (with different total charges each side). As for the field beyond the thick plates.. you know what that will be, yes?

5. Feb 14, 2013

### Ghastn

Will that be a ZERO?
I mean, the question asks for the field everywhere: that excludes the plate, right?
SO they are asking about the field outside of it! = ZERO?

6. Feb 14, 2013

### haruspex

I believe it will be zero outside the plates, but I also think the question is asking for the field inside the plates as well.

7. Feb 16, 2013

### Ghastn

Ok, so I tried this problem and I found that inside the sheets, E = Rho*x/ε.
Would that be correct?

8. Feb 16, 2013

### SammyS

Staff Emeritus
No. That does not approach zero as x → d .

How did you arrive at that answer.

You know that E = 0 for x < -d and E = 0 for x > d .

Start at x = -d and use Gauss's Law to find E for -d ≤ x ≤ 0 .