$A$ charged cork of mass $m$ suspended by a light string is placed in a uniform electric field of strength $E = (\hat{i} + \hat{j}) \times 10^5 \ NC^{-1}$ as shown in the figure. If in the equilibrium position,the tension in the string is $\frac{2mg}{(1 + \sqrt{3})}$,then the angle $\alpha$ with the vertical is:

$A$ thin-walled,spherical conducting shell $S$ of radius $R$ is given a charge $Q$. The same amount of charge $Q$ is also placed at its center $C$. Which of the following statements are 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:

Five balls numbered $1$ to $5$ are suspended using separate threads. Pairs $(1,2), (2,4)$ and $(4,1)$ show electrostatic attraction while pairs $(2,3)$ and $(4,5)$ show repulsion. Therefore,ball $1$ must be:

During lightning,a current pulse,as shown in the figure,flows from a cloud at a height of $1.5 \ km$ to the ground. If the breakdown electric field of humid air is about $400 \ kVm^{-1}$,the energy released during lightning would be (in units of $10^9 \ J$):

The dimension of $\frac{1}{2} \varepsilon_0 E^2$ (where $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field) is: