Question

Three charges are placed at the vertices of an equilateral triangle (as shown in the figure). The electric dipole moment of the system is $-\sqrt{N}qI$ $\hat{j}.$ 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 $\overset{ \rightarrow }{p}$ (due to charges at $A,B$ and $C$ ) cancel each other and vertical components add up.
So, the dipole moment of system of charges,
$\overrightarrow{ p }_{n e t}=2 p \cos 30^{\circ}(-\hat{ j })=2 q l\left(\frac{\sqrt{3}}{2}\right)(-\hat{ j })$
$=-\sqrt{3} q l \hat{j}$
$=-1.73 q l \hat{ j }$