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

Answer: 3

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