Consider the charges and the Gaussian surface shown in the figure. When calculating the electric flux through the spherical surface,the electric field is due to which of the following?

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 the net charge inside is zero?

An infinitely long wire has a uniform linear charge density $\lambda = 2 \ nC/m$. The net flux through a Gaussian cube of side length $a = \sqrt{3} \ cm$, if the wire passes through any two corners of the cube that are maximally displaced from each other, would be $x \ Nm^2 C^{-1}$, where $x$ is: [Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ SI$ units] (in $\pi$)

The flat base of a hemisphere of radius $a$ with no charge inside it lies in a horizontal plane. $A$ uniform electric field $\vec{E}$ is applied at an angle $\frac{\pi}{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is

Choose the incorrect statement:
$(a)$ The electric lines of force entering into a Gaussian surface provide negative flux.
$(b)$ $A$ charge '$q$' is placed at the centre of a cube. The flux through all the faces will be the same.
$(c)$ In a uniform electric field,the net flux through a closed Gaussian surface containing no net charge is zero.
$(d)$ When the electric field is parallel to a Gaussian surface,it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below:

Define electric flux.