$A$ point charge $2 \times 10^{-2} \, C$ is moved from $P$ to $S$ in a uniform electric field of $30 \, N C^{-1}$ directed along the positive $x$-axis. If the coordinates of $P$ and $S$ are $(1, 2, 0) \, m$ and $(0, 0, 0) \, m$ respectively,the work done by the electric field will be $......... \, mJ$.

Given $q_1 = +2 \times 10^{-8} \ C$ and $q_2 = -0.4 \times 10^{-8} \ C$. When a charge $q_3 = 0.2 \times 10^{-8} \ C$ is moved from $C$ to $D$,what is the change in the potential energy of $q_3$?

$A$ point charge $q$ moves from point $P$ to point $S$ along the path $PQRS$ (as shown in the figure) in a uniform electric field $E$ pointing parallel to the positive direction of the $X$-axis. The coordinates of the points $P, Q, R,$ and $S$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0),$ and $(0, 0, 0)$ respectively. The work done by the field in the above process is given by the expression:

Consider a spherical shell of radius $R$ with a total charge $+Q$ uniformly spread on its surface (centre of the shell lies at the origin $x=0$). Two point charges $+q$ and $-q$ are brought,one after the other,from far away and placed at $x=-a/2$ and $x=+a/2$ $(a < 2R)$,respectively. The magnitude of the work done in this process is:

Charges $5 \mu C$ and $10 \mu C$ are placed $1 \ m$ apart. Work done to bring these charges at a distance $0.5 \ m$ from each other is . . . . . . .
$(k = 9 \times 10^9 \ SI)$

Two fixed charges $A$ and $B$ of $5 \mu C$ each are separated by a distance of $6 \text{ m}$. $C$ is the midpoint of the line joining $A$ and $B$. $A$ charge $Q$ of $-5 \mu C$ is shot perpendicular to the line joining $A$ and $B$ through $C$ with a kinetic energy of $0.06 \text{ J}$. The charge $Q$ comes to rest at a point $D$. The distance $CD$ is