Find surface area of a non-conducting sheet

[dk321]

Homework Statement

A small sphere of mass m carries a charge of q. It hangs from a silk thread which makes an angle
θ with a large charged non-conducting sheet. Calculate the surface charge density on the sheet.

Homework Equations

∫E.ds

The Attempt at a Solution

I found E of the sheet to be E = σA/ε

how do i find find σ, surface charge density for this problem what is the relationship between E of the sphere and E of the sheet?

 

[EWH]

Well, I'd think about setting up an integral with circular elements, each centered on the point on the sheet closest to the ball. Each point on one of these circles will have the same force on the ball in the direction normal to the sheet. I believe the force would fall off linearly with increasing radius - increasing circle circumference linearly balanced against the inverse-square field fall-off, but the progressively increasing angles from normal-to-the-plane directly under to the ball to parallel to the sheet at infinity would give a trig term I'm too lazy to figure out. (I'm assuming the sheet is vertical. Wouldn't the length of the thread and the distance of the thread's upper suspension point from the sheet need to be given? Otherwise you could get any angle of the thread even with the ball touching the sheet. ) You'll need the equation relating total force normal to the plane to theta. Then relate charge density to force, substitute and solve.