# Charged ball attached to a charged sheet

1. Sep 14, 2009

### Oijl

1. The problem statement, all variables and given/known data
In Figure 23-43, a small, nonconducting ball of mass m = 0.80 mg and charge q = 2.2 multiplied by 10-8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ = 45° with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force of the ball and assuming that the sheet extends far vertically and into and out of the page, calculate the surface charge density σ of the sheet.

2. Relevant equations
E = surface charge density / 2epsilon

3. The attempt at a solution
Recognizing that b/c the angle of the thread is 45, the x and y components of the force of tension are equal, and therefore the electric force pushing the ball away from the wall is equal to Tx is equal to Ty is equal to weight. So F = mg.

E = F / q
F = mg
E = surface charge density / 2epsilon
mg / q = surface charge density / 2epsilon
surface charge density = mg2epsilon / q

I know m, g, and q.
I plug it in and get 6.3169 microC/m^2

But this isn't the answer, and I thought I was using the formula's correctly. Am I using the charge of the ball correctly? It seems like that would be the first place I would mess up.

Thanks for looking at this.

2. Sep 14, 2009

### rl.bhat

Can I see the figure?