$A$ point charge $q$ moves from point $P$ to $S$ along the path $PQRS$ in a uniform electric field $E$ directed parallel to the positive $X$-axis. The coordinates of points $P, Q, R,$ and $S$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0),$ and $(0, 0, 0)$ respectively. Calculate the work done by the electric field in this process.

Six point charges are placed at the vertices of a regular hexagon as shown in the figure. Three of the charges are $+q$ and the other three are $-q$. Starting from $P$ and moving clockwise,the electric field at the center $O$ is twice the electric field due to a single charge $+q$ at $R$. Which of the following arrangements of charges at $P, Q, R, S, T, U$ is correct?

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $\sigma'$,and a point charge $q_A$ is placed at the center of the shell,then choose the correct statement$(s)$.

What is the angle between the strings and the tension in the strings when two spheres are suspended in a satellite as shown in the figure?

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 $10^9 \ J$):

Two particles $X$ and $Y$, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With $Y$ at rest, $X$ begins to move towards it with initial velocity $u$. After a long time, finally