# Electric field due to plane of charge

Why the gaussian surface is "A" instead of "2A" on the right-hand side?(the photo attached below)
Due to the thickness of the sheet?

I usually find that E=σ/2ϵ0 is being frequently used but we hardly use E=σ/ϵ0.
When can I directly apply the equation E=σ/ϵ0 ?

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The one on the right is for a conducting surface. There's no charge on the other side of the surface, so there's no factor of 1/2.

Why the gaussian surface is "A" instead of "2A" on the right-hand side?(the photo attached below)
Due to the thickness of the sheet?

I usually find that E=σ/2ϵ0 is being frequently used but we hardly use E=σ/ϵ0.
When can I directly apply the equation E=σ/ϵ0 ?

I initially suspected that the RHS of the figure was just considering the flux through part of the surface, but then I saw they used the integral notation for a closed surface (meaning you have to consider both sides of the pill-box). Perhaps this shape is meant represent some charged, hollow conductor--therefore there should be no electric field inside and you only have flux through one face of the pill-box.

DuckAmuck
Chandra Prayaga
It need not be a hollow conductor. The electrostatic field within the body of a conductor is zero. So there is no field and no flux through the face within the conducting material.

It need not be a hollow conductor. The electrostatic field within the body of a conductor is zero. So there is no field and no flux through the face within the conducting material.
Yes, I agree. But this assumes that the pill-box terminates within the conductor itself. It could be possible that given illustration represents a conducting sheet, and the pill-box has ends on either side. Then I believe the equation would hold only if the sheet were a closed surface (I think that reasoning is correct). I think the illustration is a little unclear.

Chandra Prayaga