Charge Distribution on Metal Plate: How to Find Surface Charge Density?

[kuokius]

Homework Statement

Uncharged metal plate area S and thickness d located at a distance r from the point charge q and oriented perpendicular to the vector r, as shown below. Find the electric force between the plate and the charge.
The plate thickness is less, and the distance r is much greater than the linear dimensions of the plate.

http://s8.postimg.org/62esehalx/Untitled.png

Homework Equations

$$F = \frac{kq_1q_2}{r^2}$$
$$E = \frac{\sigma}{2\epsilon_0}$$

The Attempt at a Solution

[/B]
If considering a metal plate as a charge Q (because r is much greater than the linear dimensions of the plate) then the force between them would be:

$$F = \frac{kqQ}{r^2}$$

$$Q = \sigma S$$

And that's where I stop. I don't know how to find surface charge density.

 

[TSny]

If considering a metal plate as a charge Q (because r is much greater than the linear dimensions of the plate) then the force between them would be:

$$F = \frac{kqQ}{r^2}$$

What is the value of Q for the plate?

Can you see why the plate is attracted to the point charge even thought the plate is uncharged?

 

[kuokius]

What is the value of Q for the plate?

Can you see why the plate is attracted to the point charge even thought the plate is uncharged?

Because the plate is conductor and the conductor placed in electric field polarizes, i.e. one side of the plate electrifies positive and the other side negative. Also, the electric field inside a conductor is equal zero.

 

[TSny]

OK. But note that the net charge Q on the plate will always be zero. So, if you treat the plate as one point charge, Q, then $F = \frac{kqQ}{r^2}$ will give zero for the force. So, approximating the plate as one charge is too crude.

You have the right idea to model the plate as two opposite charges (a dipole). How are you going to estimate the charge induced on the surface of the plate that is nearest the point charge?