Let the electrostatic field $E$ at distance $r$ from a point charge $q$ not be an inverse square but instead an inverse cubic, e.g., $E = k \cdot \frac{q}{r^3} \hat{r}$, where $k$ is a constant.
Consider the following two statements:
$(I)$ Flux through a spherical surface enclosing the charge is $\phi = q_{\text{enclosed}} / \varepsilon_0$.
$(II)$ $A$ charge placed inside a uniformly charged shell will experience a force.
Which of the above statements are valid?

$A$ positive charge $q$ is placed at the centre of a neutral hollow cylindrical conducting shell with its cross-section as shown in the figure below. Which one of the following figures correctly indicates the induced charge distribution on the conductor? (Ignore edge effects)

If the charges inside a sphere are $+2 \times 10^{-6} \ C$,$-5 \times 10^{-6} \ C$,$-3 \times 10^{-6} \ C$,and $+6 \times 10^{-6} \ C$,what is the total electric flux passing through the sphere?

$A$ charged spherical shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the electric flux through a closed cylindrical surface of height $h$ and radius $r$, with its center coinciding with that of the shell. The center of the cylinder is a point on the axis of the cylinder equidistant from its top and bottom surfaces. Which of the following statement$(s)$ is/are correct? [$\epsilon_0$ is the permittivity of free space]
$(1)$ If $h > 2R$ and $r > R$, then $\Phi = \frac{Q}{\epsilon_0}$
$(2)$ If $h < \frac{8R}{5}$ and $r = \frac{3R}{5}$, then $\Phi = 0$
$(3)$ If $h > 2R$ and $r = \frac{4R}{5}$, then $\Phi = \frac{2Q}{5\epsilon_0}$
$(4)$ If $h > 2R$ and $r = \frac{3R}{5}$, then $\Phi = \frac{Q}{5\epsilon_0}$

The electric field in a region is given by $\vec E = a\hat i + b\hat j$. Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to the $y-z$ plane.

The spatial distribution of the electric field due to two charges $(A, B)$ is shown in the figure. Which one of the following statements is correct?