Question

If the electric flux through a gaussian surface is zero, does it necessarily mean
that
(a) the total charge inside the surface is zero?
(b) the electric field is zero at every point on the surface?
(c) the electric field lines entering into the surface is equal to the number
going out of the surface?

Answer 1

(a) and (c) are true statements.

if the electric flux through a Gaussian surface is zero,

• total charge inside the surface is zero.
• the electric field lines entering into surface is equal to the number of going out of surface.

according to Gauss's law, electric flux through the Gaussian surface is ratio of total charged enclosed inside the surface and permittivity of medium.

i.e., Φ = q_(in)/∈_0

if Φ = 0 then, q_(in) = 0

that means, total charge enclosed inside the surface is zero.

we also know, electric flux is positive when electric lines of force going out of the surface and it is negative when lines of force entering into the surface .

so, if electric flux is zero it means the electric field lines entering into the surface is equal to the number

going out of the surface.

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Answer 2

$\huge\bold\purple{Answer:-}$

No. This statement comes from Gauss' law which states that the total flux will be zero if there is zero charge within the surface. So, there could be electric fields. It is just that you will have an equal number of fields entering as leaving when there is zero charge.