Question

The electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle (as shown in figure) is $- Nq l \hat{ j }$. Determine the value of $N$.

Answer 1

The given system of charges can be considered as two dipoles of charges ' $+ q$ ' and ' $- q$ '. Let $p$ be the dipole moment of the dipole of charges $+ q$ and $- q$ (placed at point $B$ ).
The horizontal components of $\vec{p}$ (due to charges at $A , B$ and $C$ ) cancel each other and vertical components add up.
So, the net dipole moment of system of charges,
$\vec{ p }_{ nat } =2 p \cos 30^{\circ}(-\hat{ j })=2 q l\left(\frac{\sqrt{3}}{2}\right)(-\hat{ j })$
$=-\sqrt{3} q l \hat{ j } $
$=-1.73\, q l \hat{ j }$