If an electric charge $q$ is placed at the centre of a cube,then the flux associated with each surface of the cube is . . . . . . .

The electric field in a region is given by $\vec E = a\hat i + b\hat j$. Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to the $y-z$ plane.

Four charges $2 \mu C, -3 \mu C, 4 \mu C, -4 \mu C$ and $-1 \mu C$ are enclosed by a Gaussian surface of radius $2 \ m$. The net outward flux through the Gaussian surface is (in $\mu V-m$):

The adjoining diagram shows the electric lines of force emerging from a charged body. If the electric fields at $A$ and $B$ are $E_A$ and $E_B$ respectively and the distance between them is $r$,then

$A$ disk of radius $a/4$ having a uniformly distributed charge $6 \text{ C}$ is placed in the $x-y$ plane with its centre at $(-a/2, 0, 0)$. $A$ rod of length $a$ carrying a uniformly distributed charge $8 \text{ C}$ is placed on the $x$-axis from $x = a/4$ to $x = 5a/4$. Two point charges $-7 \text{ C}$ and $3 \text{ C}$ are placed at $(a/4, -a/4, 0)$ and $(-3a/4, 3a/4, 0)$,respectively. Consider a cubical surface formed by six surfaces $x = \pm a/2, y = \pm a/2, z = \pm a/2$. The electric flux through this cubical surface is

Gauss's law is true only if the force due to a charge varies as: