In a region,the electric field is given by $\overrightarrow{E}=(3 \hat{i}+5 \hat{j}+7 \hat{k}) \text{ NC}^{-1}$. The electric flux through a surface of area $3 \text{ m}^2$ in the $yz$-plane is (in $SI$ units):

If some charge is given to a solid metallic sphere,the field inside remains zero and by Gauss's law all the charge resides on the surface. Now,suppose that Coulomb's force between two charges varies as $1 / r^{3}$. Then,for a charged solid metallic sphere

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.

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

$A$ metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. $A$ charge $Q$ is placed at the centre of the spherical cavity. What will be the surface charge density on the inner surface?

If the radius of the spherical Gaussian surface is increased,then the electric flux due to a point charge enclosed by the surface: