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 $U_1/U_2$?

Write an equation for the electric potential due to an electric dipole and state its important features. Discuss its special cases.

The potential energy of a system of two equal negative point charges of $2 \mu C$ each,held $1 \ m$ apart in air,is . . . . . . . $\left( k = 9 \times 10^9 \text{ SI units} \right)$

$A$ short electric dipole has a dipole moment of $16 \times 10^{-9} \, Cm$. The electric potential due to the dipole at a point at a distance of $0.6 \, m$ from the centre of the dipole,situated on a line making an angle of $60^{\circ}$ with the dipole axis is $.........V$. (Given: $\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^{9} \, Nm^{2}/C^{2}$)

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.

Three charges are placed along the $x$-axis at $x = -a$,$x = 0$,and $x = a$ as shown in the figure. The potential energy of the system is