How Does a Charged Glass Ball Polarize a Neutral Metal Foil?

[bcjochim07]

Please help! Electric Field Problem due tomorrow

Homework Statement

We want to analyze how a charged object picks up a neutral piece of metal. A small circular disk of foil is lying flat on a table. The foil has radius R and thickness t. A glass ball w/ positive charge Q is at height h above the foil.

The ball's electric field polarizes the foil. The foil surfaces with charges +q and -q then act as the the plates of a parallel plate capacitor with separation t. But the foil is a conductor in electrostatic equilibrium so the electric field inside the foil must be zero. Write this condition as a mathematical statement and use it to find the charge on the upper surface of the foil.

Homework Equations

The Attempt at a Solution

I know that the electric field of this sphere is Q/4$$\pi$$$$\epsilon$$_or^2

Should the electric field from the ball equal the electric field from the top surface of the plate?

Ecapacitor = $$\eta$$/$$\epsilon$$_o

in the case of the foil disk $$\eta$$=q/4$$\pi$$r²

so the electric field is then q/4$$\pi$$R²$$\epsilon$$_o

If I set this equal to the electric field of the ball I get

q/4$$\pi$$R²$$\epsilon$$_o=Q/4$$\pi$$$$\epsilon$$_or^2

q=QR²/h²

The answer is actually q=QR²/4h²

Could someone help me understand this better?

 

[bcjochim07]

ok I found my mistake in the surface area of the foil... now for Q=50nC R= 1.0 mm and t=.01mm I need to find how close the ball must be to lift the foil