1. Oct 6, 2008

### bcjochim07

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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