Two charges of $5 Q$ and $-2 Q$ are situated at the points $(3 a, 0)$ and $(-5 a, 0)$ respectively. The electric flux through a sphere of radius $4a$ having center at origin is

Electric flux through a surface of area $100$ $m^2$ lying in the $xy$ plane is (in $V-m$) if $\vec E = \hat i + \sqrt 2 \hat j + \sqrt 3 \hat k$

A charged body has an electric flux $\phi$ associated with it. The body is now placed inside a metallic container. The flux $\phi$, outside the container will be

The electric flux for Gaussian surface A that enclose the charged particles in free space is (given $q_1$ = $-14\, nC$, $q_2$ = $78.85\, nC$, $q_3$ = $-56 \,nC$)

Four closed surfaces and corresponding charge distributions are shown below

Let the respective electric fluxes through the surfaces be ${\phi _1},{\phi _2},{\phi _3}$ and ${\phi _4}$ . Then

As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C$. The magnitude of charge within the cuboid is $n \varepsilon_0 C$. The value of $n$ is $............$ (if dimension of cuboid is $1 \times 2 \times 3 \;m ^3$ )