23.12
Consider a thin, infinite conducting plate having a positive charge.
In the absence of an external field, the charges spread out on the plate with a uniform surface charge density. It sets up an electric field on both sides, directed away from the plate, given as surface charge density over two times the vacuum permittivity.
Suppose an identical negatively charged plate is brought closer to the positively charged plate. The charges on both plates attract each other.
In the region between the plates, the electric field due to both plates have the same direction, and as a result, fields add up to give a net electric field. However, on either side of the two plates, the fields are in opposite directions, canceling each other.
This electric field pattern is analogous to a charged parallel plate capacitor.
Now, if the negatively charged plate is replaced with an identical positively charged plate, the net field between the plates cancels each other and is zero. However, on either side, the fields add up.
Gauss' law relates the electric flux through a closed surface to the net charge enclosed by that surface. Gauss's law can be applied to find the elect…
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