. 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.
By Gauss's law of electro statics, ∮E.ds=ϵ0q Consider a Gaussian surface enclosing charges q1, q2, q3 and q4 as shown in figure. q1+q2+q3=0 But, electric field on R.H.S. due to q4 will not be zero. But, on the L.H.S., it will be zero. So the statement is true. If electric field on Gaussian surface is zero then, in the above case, it is possible only when q4=0. i.e. if everywhere, on Gaussian surface, electric field is zero then net charge will be zero.
