Question

If the total charge enclosed by a surface is zero, does it imply that the elecric 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.

Answer 1

According to Gauss’ law, the flux associated with any closed surface is given by ${\displaystyle {\int }_s}$ E.dS = ${\displaystyle \frac{q_{enclosed}}{{\epsilon }_0}}$. The term ${\displaystyle q_{enclosed}}$ on the right side of the equation includes the sum of all charges enclosed by the surface called (Gaussian surface).

In the left side equation, the electric field is due to all the charges present both inside as well as outside the Gaussian surface.

Thus, despite being total charge enclosed by a surface zero, it doesn’t imply that the electric field everywhere on the surface is zero, the field may be normal to the surface.

Also, conversely if the electric field everywhere on a surface is zero.