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.
If the total charge is zero enclosed by a surface, it does not necessarily mean that the electric field is also zero enclosed by the surface. The electric field can be perpendicular to the surface. While conversely, it does imply that the electric field is zero on the surface.