The inward and outward electric flux for a closed surface in units of $N \cdot m^2/C$ are respectively $8 \times 10^3$ and $4 \times 10^3$. Then the total charge inside the surface is [where $\varepsilon_0$ = permittivity constant].

$A$ rectangular surface of sides $10 \,cm$ and $15 \,cm$ is placed inside a uniform electric field of $25 \,V/m$,such that the surface makes an angle of $30^{\circ}$ with the direction of the electric field. Find the flux of the electric field through the rectangular surface in $Nm^2/C$.

$A$ 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 $x = +a/2$.

$A$ charged particle $q$ is placed at the centre $O$ of a cube of side length $L$ $(A, B, C, D, E, F, G, H)$. Another identical charge $q$ is placed at a distance $L$ from $O$, outside the cube, as shown in the figure. The electric flux through the face $BGFC$ is

$A$ thin spherical shell of radius $R$ and surface charge density $\sigma$ is placed in a cube of side $5R$ with their centers coinciding. The electric flux through one face of the cube is $(\varepsilon_0 = \text{Permittivity of free space})$

The electric field in a region is given by $\vec{E}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \ N/C$. The flux of the field through a rectangular surface parallel to the $x-z$ plane is $6.0 \ N m^2 C^{-1}$. The area of the surface is . . . . . . $cm^2$.