An electric dipole is as shown in the figure. The electric potential at point $P$ due to the dipole is $[\epsilon_0 = \text{permittivity of free space}]$.

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 $U_1/U_2$?

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

The condition for minimum potential energy of an electric dipole in a uniform electric field is ......

Two charges $+3.2 \times 10^{-19} \, C$ and $-3.2 \times 10^{-19} \, C$ kept $2.4 \, \mathring{A}$ apart form a dipole. If it is kept in a uniform electric field of intensity $4 \times 10^5 \, V/m$,what will be its electrical potential energy in stable equilibrium?

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: