Question

If E=0, at all points of a closed surface. The total charge enclosed by the surface is zero.
A. True
B. False

Answer 1

In order to find the electric field we use integration usually. But if integration over the body becomes complicated then we use a simple law called gauss law in order to find out the electric field due to the charged body. Integration for non uniform shaped bodies will be difficult. Then gauss law might help. We solve this problem using gauss law.
Formula used:
$\int {E.dA} = \dfrac{{{q_{in}}}}{{{\varepsilon _0}}}$

Complete answer:
There are some limitations where we can apply gauss law. In order to apply gauss law we will consider a gaussian surface. Now that gaussian surface should not pass through the point charge or discrete charge. It can pass through continuous charge. The electric field on that gaussian surface will be due to the charges inside and outside the gaussian surface, but the charge we take for the application of the gauss law should be the charge inside the gaussian surface.
We can take any gaussian surface. But if we need to find an electric field at the point on gaussian surface then the conditions to be followed is, electric field but be same everywhere on the gaussian surface and electric field must be either parallel or perpendicular to gaussian surface and the gaussian surface must be symmetrical.
Gauss law will be
$\int {E.dA} = \dfrac{{{q_{in}}}}{{{\varepsilon _0}}}$
From the above formula it is clear that if E is zero everywhere, then flux will be zero and charge enclosed will be zero then. Hence the given statement is true.

Option A is correct.

Note:
One thing to be noted is the electric field in the flux formula is due to charges inside and outside the gaussian surface but charge in flux formula is only the charge inside the gaussian surface. If charge enclosed is zero, that doesn’t mean the electric field everywhere is zero. The best example for this is the gaussian surface around dipole.