$A$ charge $q$ is placed at one corner of a cube as shown in the figure. The flux of the electrostatic field $\overrightarrow{E}$ through the shaded area is ...... .

Consider four closed surfaces $S_1, S_2, S_3,$ and $S_4$ each enclosing the same charge $q_1$. Compare the electric flux through these surfaces.

$A$ uniform electric field $E = 3 \times 10^5 \text{ NC}^{-1}$ is acting along the positive $Y$-axis. The electric flux through a rectangle of area $10 \text{ cm} \times 30 \text{ cm}$ whose plane is parallel to the $ZX$-plane is

Electric charge is uniformly distributed along a long straight wire of radius $1\, mm$. The charge per $cm$ length of the wire is $Q$ $coulomb$. Another cylindrical surface of radius $50\, cm$ and length $1\, m$ symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is

$Assertion (A):$ $A$ charge $q$ is placed at a height $h/4$ above the center of a square of side $b$. The flux associated with the square is independent of the side length $b$.
$Reason (R):$ Gauss's law is independent of the size of the Gaussian surface.

The linear charge density of a wire is $8.85 \ \mu C/m$. The radius and height of the cylinder are $3 \ m$ and $4 \ m$ respectively. Find the electric flux passing through the cylinder.