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## Homework Statement

A 10.0 g piece of Styrofoam carries a net charge of -0.700 [itex]\mu[/itex]C and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet?

## Homework Equations

F

_{e}= [itex]\frac{KqQ}{r^2}[/itex] (q is the charge of the styrofoam- given, and Q is the total charge of the plastic sheet. K is Coulumbs Constant = 8.99x10^9)

F

_{g}= mg

σ = [itex]\frac{Q}{A}[/itex] (Q is the total charge of the sheet, A is its area)

[itex]\Phi[/itex] = [itex]\oint[/itex] E[itex]\cdot[/itex]dA = q

_{in}/ε

_{0}(E is the electric field. dA is an infinitesimal area VECTOR hence the dot product. q

_{in}is the total charge inside a Gausian surface. ε

_{0}is the permittivity of free space which is equal to 1/(K4[itex]\pi[/itex]) which means 1/ε

_{0}= K4[itex]\pi[/itex]

## The Attempt at a Solution

Obviously since the Styrofoam is floating at equilibrium F

_{g}= F

_{e}and I set those equal to each other, but since I don't know "r" - the height that the Styrofoam is suspended at, or "A" - the area of the plastic sheet, or "Q" (the total charge of the sheet) I don't know how to solve for σ. I couldn't come up with a Gaussian surface that would make E and A vectors parallel to simplify the surface integral, so I don't know if I can do anything with that equation. Thank you for taking the time to read and hopefully help.