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# Gauss's Law - field of infinite plane sheet watch

1. Use Gauss's Law to calculate the field of an infinite plane sheet of surface charge density σ0.

The solution is, where A=area:

2EA=(σ/ ϵ0)A

E=σ/2ϵ0

Why is there a '2' in the solution? I know it's something to do with twice the electric field. Is it because there are two sides to the sheet surface?

Thank you.
2. You use a cylinder as your closed surface. To have symmetry, the ends of the cylinder have to be on opposite sides of the sheet. There are two ends of the cylinder, which gives you the 2A.
3. (Original post by little pixie)
Use Gauss's Law to calculate the field of an infinite plane sheet of surface charge density σ0.

The solution is, where A=area:

2EA=(σ/ ϵ0)A

E=σ/2ϵ0

Why is there a '2' in the solution? I know it's something to do with twice the electric field. Is it because there are two sides to the sheet surface?

Thank you.
This is what your Gaussian surface is:

By symmetry is electric field is in the direction of the surface normal, but this is true for both sides of the sheet, so you get twice the contribution to the flux, due to the ends of the cylinder.
4. Thanks very much dknt!

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Updated: March 28, 2013
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