$Assertion\,(A):$ A charge $q$ is placed on a height $h / 4$ above the centre of a square of side b. The flux associated with the square is independent of side length.

$Reason\,(R):$ Gauss's law is independent of size of the Gaussian surface.

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?

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

If $\oint_s \vec{E} \cdot \overrightarrow{d S}=0$ over a surface, then:

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?

$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$

$(B)$ The z-component of the electric field is zero at all the points on the surface of the shell

$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$

$(D)$ The electric field is normal to the surface of the shell at all points

Why do electric field lines not form closed loop ?