Consider a cube of side length '$a$' centered at the origin. It is enclosed by three fixed point charges: $(-q)$ at $(0, -a/4, 0)$,$(+3q)$ at $(0, 0, 0)$,and $(-q)$ at $(0, a/4, 0)$. Choose the correct option.

In a region,the intensity of an electric field is given by $\overrightarrow{E}=(2 \hat{i}+3 \hat{j}+\hat{k}) \text{ NC}^{-1}$. The electric flux through a surface of area $10 \hat{i} \text{ m}^2$ in the region is

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?

$A$ charge $q$ is placed at the center of the circular base of an inverted cone of height $h$ and base radius $R$. The cone is capped by a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 \epsilon_0}$ (in $SI$ units). The value of $n$ is. . . .

Flux coming out from a positive charge of $8 \ C$,placed in a medium of dielectric constant $4$ is

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface $S$ is