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.

Explanation

If the net charge enclosed by a surface is zero, then we know, according to Gauss.s theorem, that the total electric flux associated with the given surface will be zero, but it does not imply that the electric field intensity everywhere on this surface will be zero. The total electric flux can be zero due to the angle between the electric field intensity and the area vector being `90^@`. The total electric flux can also be zero due to cancellation of the positive and negative flux linked with the different portions of the surface. On the other hand, if the electric field intensity everywhere on the Gaussian surface is zero, then the electric flux will certainly be zero. In this case, net enclosed charge must be zero to satisfy Gauss.s theorem.