Why do electric field lines not form closed loop ?

Consider a uniform electric field $E =3 \times 10^{3} i\; N / C .$

$(a)$ What is the flux of this field through a square of $10 \;cm$ on a side whose plane is parallel to the $y z$ plane?

$(b)$ What is the flux through the same square if the normal to its plane makes a $60^{\circ}$ angle with the $x -$axis?

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

A point charge of $2.0\; \mu \,C$ is at the centre of a cubic Gaussian surface $9.0\; cm$ on edge. What is the net electric flux through the surface?

An electric field is uniform, and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i }\; N/C$ for $x\,>\,0$ and $E =  - 200\hat i\;N/C$ for $x < 0 .$ A right ctrcular cyllnder of length $20 \;cm$ and radius $5\; cm$ has its centre at the origin and its axis along the $x$ -axis so that one face is at $x=+10\; cm$ and the other is at $x=-10\; cm$

$(a)$ What is the net outward flux through each flat face?

$(b)$ What is the flux through the side of the cylinder?

$(c)$ What is the net outward flux through the cylinder?

$(d)$ What is the net charge inside the cyllnder?

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. $E =k \cdot \frac{q}{r^{3}} \hat{ r }$, here $k$ 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 uniformly charged shell will experience a force.

Which of the above statements are valid?