# Surface Charge Density and electron

1. Oct 1, 2008

### grouchy

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

an electron with mass m = 9.11 x 10^-31 is released at rest near a very large positively charged non-conducting charged sheet lying horizontally. What should the surface charge density on this sheet be to keep the electron balanced at rest above the ground? Is it above or below the sheet?

2. Relevant equations

F = qE
d(density) = Eϵ

3. The attempt at a solution

qE = mg
E = (mg)/ q

d = Eϵ
d = (mgϵ )/q

When I plug in all my values I get 4.938 x 10^-22 C/m^2

but the answer is 9.88 x 10^-22 (if I multiply my answer by 2 it would be right but I dont think thats how I need to do it.)

2. Oct 1, 2008

### tiny-tim

Hi grouchy!

I'm not sure what you've done, but I think you've used the equation for a point (or nearly point) charge.

This is a spread-out charge, so you'll have to integrate over the whole plane.

3. Oct 1, 2008

### grouchy

I found my mistake, I used the equation for conducting sheet of charge E = d/ϵ

but the problem says non conducting which is E = d/2ϵ which tells me its right when I multiply by 2 :)