An electric field is given by $\vec{E} = (6 \hat{i} + 5 \hat{j} + 3 \hat{k}) \ N/C$. The electric flux through a surface area $\vec{A} = 30 \hat{i} \ m^2$ (in $SI$ units) is:

$A$ point charge is distributed in a small volume. The electric flux through a spherical surface of radius $10 \ cm$ enclosing the charge is $20 \ Vm$. What is the electric flux through a concentric spherical surface of radius $20 \ cm$?

$A$ point charge $q$ is placed at a distance $a/2$ directly above the center of a square of side $a$. The electric flux through the square is:

Two point charges $2q$ and $q$ are placed at vertex $A$ and the centre of face $CDEF$ of the cube, respectively, as shown in the figure. The electric flux passing through the cube is:

$A$ uniformly charged conducting sphere of diameter $14 \ cm$ has a surface charge density of $40 \ \mu C/m^2$. The total electric flux leaving the surface of the sphere is nearly (Permittivity of free space $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2/N \cdot m^2$)

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