If the total charge enclosed by a surface is zero, does it imply that the electric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.

Question

If the total charge enclosed by a surface is zero, does it imply that the electric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.

Philoid · Accepted Answer

Assuming that there are no charges outside the given enclosed surface, the total charge enclosed by this surface is zero. This implies that there are dipoles in the enclosed surface. We thus know that there will be electric field everywhere on the surface and it is not zero.

If the electric field everywhere on the surface is zero, it implies that there are no net electric charges inside or outside the given surface.