Gauss’s law states that

In a region of space the electric field is given by $\vec E = 8\hat i + 4\hat j+ 3\hat k$. The electric flux through a surface of area $100\, units$ in the $x-y$ plane is….$units$

A point charge causes an electric flux of $-1.0 \times 10^{3}\; N\;m ^{2} / C$ to pass through a spherical Gaussian surface of $10.0\; cm$ radius centred on the charge.

$(a)$ If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

$(b)$ What is the value of the point charge?

Gauss’s law is true only if force due to a charge varies as

An electric field $\overrightarrow{\mathrm{E}}=(2 \mathrm{xi}) \mathrm{NC}^{-1}$ exists in space. $\mathrm{A}$ cube of side $2 \mathrm{~m}$ is placed in the space as per figure given below. The electric flux through the cube is ……………… $\mathrm{Nm}^2 / \mathrm{C}$