An electric dipole with dipole moment $p$ is placed in an electric field of intensity $E$. Initially,the dipole is parallel to the field. What is the work done by an external agent to rotate the dipole by $180^{\circ}$ in the electric field?

When a negative charge is taken at a height from the Earth's surface,its potential energy:

Three charges $Q$,$+q$,and $+q$ are placed at the vertices of a right-angled triangle as shown. The net electrostatic potential energy of the configuration is zero. The value of $Q$ is

In the first configuration $(1)$ as shown in the figure,four identical charges $(q_0)$ are kept at the corners $A, B, C$ and $D$ of a square of side length $a$. In the second configuration $(2)$,the same charges are shifted to the midpoints $G, E, H$ and $F$ of the sides of the square. If $K = \frac{1}{4 \pi \varepsilon_0}$,the difference between the potential energies of configuration $(2)$ and $(1)$ is given by:

The electrostatic potential due to an electric dipole at a distance '$r$' varies as:

Two charges $-q$ each are separated by a distance $2d$. $A$ third charge $+q$ is kept at the midpoint $O$. Find the potential energy of $+q$ as a function of a small distance $x$ from $O$ due to the $-q$ charges. Sketch the $P.E.$ versus $x$ graph and convince yourself that the charge at $O$ is in an unstable equilibrium.