An electric dipole with dipole moment $\vec p$ is placed in a uniform electric field $\vec E$. The work done in rotating the dipole by $90^\circ$ from its initial equilibrium position is:

Two negative charges,each of magnitude $q$,are separated by a distance of $2r$. $A$ positive charge $q$ is placed at their center. The potential energy of the system is $U_1$. If the two negative charges are interchanged with the positive charge such that the new potential energy is $U_2$,what is the ratio $U_1/U_2$?

Derive the formula for the electric potential energy of a system of two point charges.

Three point charges $1 \text{ C}, 2 \text{ C}$ and $3 \text{ C}$ are placed at the corners of an equilateral triangle of side $1 \text{ m}$. The work done to move these charges to the corners of another equilateral triangle of side $0.5 \text{ m}$ is

Three point charges $+q, +2q$ and $+Q$ are placed at the vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $Q$ in terms of $q$ is:

The work done required to assemble the four charges at the corners of a square of side $a$, as shown in the figure, is: