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I can't figure out how to find the charge density for the following problem:

A conductor is placed in an external electrostatic field. The external field is uniform before the conductor is placed within it. The conductor is completely isolated from any source of current or charge.

Assume that at some point just outside the surface of the conductor, the electric field has magnitude E and is directed toward the surface of the conductor. What is the charge density n on the surface of the conductor at that point?

I'm supposed to express my answer in terms of $E$ and $\epsilon_0$.

I know that Electric Flux = Normal Angle x Electric Field x cos(theta), but I don't know how to relate this to charge density?

What am I missing to solve this problem? This is very basic, I know, but I'm stumped. The hints on Mastering Physics also aren't really helping.

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For one, I'm thinking the problem wants you to assume the external field is normal to the surface, so you wouldn't need any cosine. If not, the field from an infinite surface with a charge on it would be in a different angle from the external field and give a resultant non-normal electric field. Also, given the wording of the problem I think they intend the external field to be opposite direction of the field from the surface charge. Resultant field should be in direction of external field too. – AlanSE Sep 11 '12 at 22:42
@AlanSE that could be a reasonably good answer – David Zaslavsky♦ Sep 12 '12 at 0:02

1 Answer

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Consider a tiny part of th conductor's surface. Then the field at this part is approximately uniform so this is like an infinite parallel plane: $E = \sigma/2\epsilon_0$. Whence, the surface charge density is $\sigma = 2\epsilon_0 E$. since it is a conductor, there is no volumetric charges: everything is concentrated in the surface.

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