You are given a dipole of charge $+q$ and $-q$ separated by a distance $2R$. $A$ sphere '$A$' of radius ' $R$ ' passes through the centre of the dipole as shown below and another sphere '$B$' of radius ' $2R$ ' passes through the charge $+q$. Then the electric flux through the sphere '$A$' is

The flat base of a hemisphere of radius $a$ with no charge inside it lies in a horizontal plane. $A$ uniform electric field $\vec{E}$ is applied at an angle $\frac{\pi}{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is

$A$ point charge of $+12 \,\mu C$ is at a distance $6 \,cm$ vertically above the centre of a square of side $12 \,cm$ as shown in the figure. The magnitude of the electric flux through the square will be ....... $\times 10^{3} \,Nm^{2}/C$.

$A$ cubical region of side $a$ has its centre at the origin. It encloses three fixed point charges,$-q$ at $(0, -a/4, 0)$,$+3q$ at $(0, 0, 0)$,and $-q$ at $(0, +a/4, 0)$. Choose the correct option$(s)$.
$(A)$ The net electric flux crossing the plane $x = +a/2$ is equal to the net electric flux crossing the plane $x = -a/2$.
$(B)$ The net electric flux crossing the plane $y = +a/2$ is more than the net electric flux crossing the plane $y = -a/2$.
$(C)$ The net electric flux crossing the entire region is $\frac{q}{\varepsilon_0}$.
$(D)$ The net electric flux crossing the plane $z = +a/2$ is equal to the net electric flux crossing the plane $x = +a/2$.

Discuss some points about Gauss's law.

In a region,the intensity of an electric field is given by $\overrightarrow{E}=(2 \hat{i}+3 \hat{j}+\hat{k}) \text{ NC}^{-1}$. The electric flux through a surface of area $10 \hat{i} \text{ m}^2$ in the region is