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In finding the electric field using Gauss law the formula |E| = q_enc/(ε0 |A|) is applicable. In the formula ε0 is permittivity of free space, A is the area of Gaussian surface and q_enc is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation ?

1. For any choice of Gaussian surface.
2. Only when the Gaussian surface is an equipotential surface.
3. Only when |E| is constant on the surface.
4. Only when the Gaussian surface is an equipotential surface and |E| is constant on the surface.

Correct answer: Only when the Gaussian surface is an equipotential surface and |E| is constant on the surface.

Solution

The simple form |E| = q_enc/(eps0|A|) requires that E be perpendicular to the surface (so the surface is equipotential) and that |E| be constant over it, so that the flux integral reduces to |E||A|. Both conditions must hold.

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