Gauss's law is given by ${\epsilon _0}\oint {\vec E \cdot d\vec s} = q$. If the net charge enclosed by a Gaussian surface is zero,then .......

$A$ uniformly charged conducting sphere of $2.4\; m$ diameter has a surface charge density of $80.0\; \mu C/m^2$.
$(a)$ Find the charge on the sphere.
$(b)$ What is the total electric flux leaving the surface of the sphere?

If a charge $Q$ is placed at the corner of a cube,what is the electric flux passing through one of its faces?

$A$ 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

The electric field in a region of space is given by $\vec{E} = (5\hat{i} + 2\hat{j}) \text{ N/C}$. Calculate the electric flux through a surface of area $2 \text{ m}^2$ lying in the $YZ$-plane.

$A$ charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge $a$ as shown in the figure. The electric flux through the square surface is