Uniform Charge Density on a Plastic Sheet

[Solidification]

I've been struggling over this the entire weekend and am about to rip my hair out.

Suppose we have some object with a mass M and a charge Q. It floats above the center of a large horizontal plastic sheet with a uniform charge density on its surface. What is the charge-per-area (sigma) on the plastic sheet?

Every bit of "help" I've found all dealt with spheres and two plates with some distance between each other, or some point located some given distance away from a plane, etc. I don't know where to start with this. I attempted the E = sigma / (2*epsilon), where epsilon is the permittivity of free space (I apologize; I do not understand how to input Greek letters and mathematical signs on forums).

I think that's right, but the 2 might be unnecessary. From there, I knew I had to replace E with something else. That I'm not sure of because I don't know of anything that relates a field of Energy with mass, except that a = qE/m. Since it is hovering, though, I'd suspect a = 0, so that's useless to me. My force equations seem useless because they've all required some radius, but there's no specification.

I'm more interested on just where to start (one step beyond the E = sigma / (2*epsilon), assuming that's even right to begin with). Any help is greatly appreciated.

 

[Psi-String]

The equation e= \frac{\sigma}{2 \epsilon_0} is valid only when the sheet is very large, comparing to the distance betwwen the sheet and the object. In this case, I think using this is logical.

a = \frac{qE}{m} what is this acceleration mean? It's not the object's resultant acceleration

I think equillibrium can solve this problem.

 

[Solidification]

You were absolutely right. Thank you. I had thought the acceleration WAS the resultant acceleration. It certainly implies that in my physics books.