$A$ 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.

Three point charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.

$A$ particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle loses contact with the sphere when the line joining the center of the sphere and the particle makes an angle $45^{\circ}$ with the vertical. The ratio $\frac{qE}{mg}$ is:

Consider two point charges of equal magnitude and opposite sign separated by a certain distance. The neutral point due to them

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \text{ C/m}^2$ is placed on the $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \text{ C/m}$ is placed at the $z=4 \text{ m}$ plane and is parallel to the $y$-axis. If the magnitude values satisfy $|\sigma_s| = 2|\lambda_e|$,then at the point $(0, 0, 2)$,the ratio of the magnitudes of the electric field values due to the sheet charge to that of the line charge is $\pi \sqrt{n} : 1$. The value of $n$ is:

Two equal negative charges are fixed at the points $(0, a)$ and $(0, -a)$ on the $y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x$-axis. The charge $Q$ will