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 $q_3$?

Obtain the equation for the electric potential energy of a single charge in an external electric field.

$A$ negatively charged particle is released from rest in a uniform electric field. The electric potential energy of the charge:

Two point charges of $5 \ \mu C$ and $10 \ \mu C$ are separated by a distance of $1 \ m$. The work done to bring them to a distance of $0.5 \ m$ is:

Obtain the equation for the electric potential energy of a system of two electric charges in an external electric field.

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: