# Homework Help: Electrostatic pressure for a sheet

1. Nov 26, 2015

### erisedk

1. The problem statement, all variables and given/known data
An infinitely large layer of charge of uniform thickness t is placed normal to an existing uniform electric field. The charge on the sheet alters the electric field so that it still remains uniform on both sides of the sheet and assumes values E1 and E2 (E1 on the left, pointing in the +ve x direction, E2 on the right, also pointing in the +ve x direction). The charge distribution in the layer is not uniform and depends only on the distance from its faces. Find the expression for the force F per unit area experienced by the charged layer.

2. Relevant equations
Electrostatic pressure = 1/2 ε E2

3. The attempt at a solution
Assuming E to be the original electric field, Elayer to be the EF due to the layer, and the layer to be positively charged:
On the left side of the layer,
E-Elayer = E1
Right side:
E+Elayer = E2
E = (E1 + E2)/2
Using Gauss (taking a Gaussian pillbox shaped surface that protrudes out from both sides of the layer)
-E1A + E2A = Q/ε (Q is the charge inside the Gaussian surface)
So,
E2 - E1 = Q/Aε
So, the force experienced by the charge layer per unit area is
F/A = (Q/A)E (cos the charged layer isn't affected by Elayer, i.e. it's own field)
Substituting in Q/A and E from above,
F/A = (ε (E22 - E12) ) / 2

Which is correct. But looking at the answer, I was wondering if someone could offer me an idea of how to approach this using electrostatic pressure, because I've seen it in terms of spheres, never in terms of sheets of charge. And looking at the directions of the EF on both sides (they're pointing in the same direction), it feels like the pressures might add up, but instead they're getting subtracted, so I think I lack a clear conceptual understanding of electrostatic pressure.

2. Dec 1, 2015