$A$ charged particle of charge $Q$ is held fixed and another charged particle of mass $m$ and charge $q$ (of the same sign) is released from a distance $r$. The impulse of the force exerted by the external agent on the fixed charge by the time the distance between $Q$ and $q$ becomes $2r$ is:

Six charges,three positive and three negative of equal magnitude,are placed at the corners of a regular hexagon such that the electric field at the center $O$ is double the electric field obtained when only a charge of the same magnitude is placed at $R$. What are the charges at $P, Q, R, S, T,$ and $U$ respectively?

$A$ 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:

This question contains Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
Statement-$1$ : For a charged particle moving from point $P$ to point $Q$,the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement-$2$ : The net work done by a conservative force on an object moving along a closed loop is zero.

$A$ metallic shell has a point charge '$q$' kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force?

Two point charges $4\,\mu C$ and $-1\,\mu C$ are kept at a distance of $3\ m$ from each other. What is the electric potential at the point where the electric field is zero?