# The electric field of infinite sheets

I am trying to understand electric fields of conductors.

Say that there is an infinite sheet of uniform positive charge; parallel to it lies a infinite, uncharged conducting sheet. What would the field look like between the sheets? Beyond the sheets? I would guess that the uniformly charged sheet would induce a uniformly distributed negative charge on the conducting sheet on the side closer to it, but I don't understand how the induced positive charge would distribute itself in the conducting sheet. Or how the positive charge would then affect the field.

Thanks.

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cnh1995
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but I don't understand how the induced positive charge would distribute itself in the conducting sheet. Or how the positive charge would then affect the field.
It will be on the other surface(outer surface, far from the sheet) of the conducting sheet. These induced charges will make the E field inside the conducting sheet 0. Electric field lines from the charged sheet will terminate at the -ve induced charge on the conducting sheet and will reappear from the +ve induced charge on the other surface of the conducting sheet.

Conservation
Okay. That makes sense; That would make E field coming out from the opposite surface same as the E field going in, and that's consistent with Gauss's law.

What I fail to see is how this distribution of induced charges will result a field of 0 inside the conductor. If there is an infinite positive surface charge on one side of the conducting sheet and infinite negative surface charge on the other side of the conducting sheet, shouldn't there be a field inside the conducting sheet?

cnh1995
Homework Helper
Gold Member
shouldn't there be a field inside the conducting sheet?
Yes. And that field exactly cancels the field due to the charged sheet, making net E field inside the conducting sheet zero. This is why electric field inside a conductor placed in an external electric field is always 0.

Conservation