If the electric field is given by $\vec{E} = (5 \hat{i} + 4 \hat{j} + 9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units):

$A$ disk of radius $a/4$ having a uniformly distributed charge $6 \text{ C}$ is placed in the $x-y$ plane with its centre at $(-a/2, 0, 0)$. $A$ rod of length $a$ carrying a uniformly distributed charge $8 \text{ C}$ is placed on the $x$-axis from $x = a/4$ to $x = 5a/4$. Two point charges $-7 \text{ C}$ and $3 \text{ C}$ are placed at $(a/4, -a/4, 0)$ and $(-3a/4, 3a/4, 0)$,respectively. Consider a cubical surface formed by six surfaces $x = \pm a/2, y = \pm a/2, z = \pm a/2$. The electric flux through this cubical surface is

In a uniform electric field,a cube of side $1 \ cm$ is placed. The total energy stored in the cube is $8.85 \ \mu J$. The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is.

$A$ cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

$A$ uniformly charged conducting sphere of $2.4\; m$ diameter has a surface charge density of $80.0\; \mu C/m^2$.
$(a)$ Find the charge on the sphere.
$(b)$ What is the total electric flux leaving the surface of the sphere?

$A$ point charge $q$ is placed at a distance $\frac{a}{2}$ directly above the centre of a square of side $a$. The electric flux through the square is