$q_1, q_2, q_3$ and $q_4$ are point charges located as shown in the figure,and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to Gauss's law?

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?

$A$ metallic sphere of radius $R$ carrying a charge $q$ is kept at a certain distance from another metallic sphere of radius $R/4$ carrying a charge $Q$. What is the electric flux at any point inside the metallic sphere of radius $R$ due to the sphere of radius $R/4$?

What is called a Gaussian surface?

An electric field is uniform,and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E = 200 \hat{i} \; N/C$ for $x > 0$ and $E = -200 \hat{i} \; N/C$ for $x < 0$. $A$ right circular cylinder of length $20 \; cm$ and radius $5 \; cm$ has its centre at the origin and its axis along the $x$-axis so that one face is at $x = +10 \; cm$ and the other is at $x = -10 \; cm$.
$(a)$ What is the net outward flux through each flat face?
$(b)$ What is the flux through the side of the cylinder?
$(c)$ What is the net outward flux through the cylinder?
$(d)$ What is the net charge inside the cylinder?

The electric field in a region is given by $\overrightarrow{E} = (\frac{3}{5} E_{0} \hat{i} + \frac{4}{5} E_{0} \hat{j}) \, N/C$. The ratio of the flux of this field through a rectangular surface of area $0.2 \, m^{2}$ (parallel to the $y-z$ plane) to that through a surface of area $0.3 \, m^{2}$ (parallel to the $x-z$ plane) is $a : b$,where $a = \dots$ [Here $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along the $x, y$ and $z$-axes respectively].