If the net flux through a gaussian surface is zero, the following four statements could be true. which of the statements must be true? there are no charges inside the surface. the net charge inside the surface is zero. the electric field is zero everywhere on the surface. the number of electric field lines entering the surface equals the number leaving the surface.

The statements which are true are as follows:

Explanation:

The electric flux through a surface is defined as the number of electric field lines passing through the unit area of that surface normally.

It is given as

According to Gauss' law, it is given as

where,

is the net charge enclosed by the surface.

is the electrical permittivity of free space.

Statement 1: There are no charges inside the surface.

It is not a necessary condition for electric flux through that surface to be zero because the even if there is some charge present inside the surface such that the net charge(sum of all charges) inside the surface is zero, then the electric flux through that surface is also zero.  

Thus, this statement need not to be necessarily true.

Statement 2: The net charge inside the surface is zero.

As mentioned in the above part of the answer, if the net charge inside the surface is zero then the electric flux through that surface must be zero.

Thus, this statement must be true.

Statement 3: The electric field is zero everywhere on the surface.

According to the equation (1), the electric flux through that surface must be zero.

Thus, this statement must be true.

Statement 4: The number of electric field lines entering the surface equals the number leaving the surface.

If the number of electric field lines passing through that surface is equal to that of electric field lines leaving that surface then it means there is not any charge present inside the surface. In that case, the electric flux through the surface is zero.

Thus, this statement must be true.