$A$ glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to $X$-rays for a short period. Then

$A$ thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_0$. $A$ hole with a small area $\alpha 4 \pi R^2$ (where $\alpha \ll 1$) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

The electric field is in the direction of the $x$-axis. The work done to move a charge of $0.2 \ C$ by a distance of $2 \ m$ at an angle of $60^\circ$ with the $x$-axis is $4 \ J$. What is the value of the electric field $E$ in $N/C$?

Point charges are placed at the vertices of a regular hexagon with center $O$ and side length $L$ as shown in the figure. Given $K = \frac{q}{4\pi \epsilon_0 L^2}$,which of the following statements is correct?

Identify the correct statements:
$A$. Electrostatic field lines form closed loops.
$B$. The electric field lines point radially outward when charge is greater than zero.
$C$. The Gauss-Law is valid only for inverse-square force.
$D$. The work done in moving a charged particle in a static electric field around a closed path is zero.
$E$. The motion of a particle under Coulomb's force must take place in a plane.
Choose the correct answer from the options given below:

Two charged particles,each of mass $3 \ g$ and charge $0.2 \ \mu C$,stay in (vacuum) equilibrium on a horizontal surface with a separation of $20 \ cm$. The coefficient of friction is $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \ Nm^2 C^{-2}\right]$ and $\left(g=10 \ ms^{-2}\right)$.