Three point charges $3 \text{ nC}$,$6 \text{ nC}$,and $9 \text{ nC}$ are placed at the corners of an equilateral triangle of side $0.1 \text{ m}$. The potential energy of the system is:

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?

Two electric dipoles $A$ and $B$ with respective dipole moments $\overrightarrow {{d_A}} = - 4\,qa\,\hat i$ and $\overrightarrow {{d_B}} = 2\,qa\,\hat i$ are placed on the $x-$ axis with a separation $R$,as shown in the figure. The distance from $A$ at which both of them produce the same potential is

$A$ molecule of a substance has a permanent electric dipole moment of magnitude $10^{-29} \; C \; m$. $A$ mole of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude $10^{6} \; V \; m^{-1}$. The direction of the field is suddenly changed by an angle of $60^{\circ}$. Estimate the heat released (in $J$) by the substance in aligning its dipoles along the new direction of the field. For simplicity,assume $100 \%$ polarization of the sample.

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

What is the potential energy of two equal positive point charges of $1\,\mu C$ each,held $1\, m$ apart in air?