Question

Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

Answer 1

Let $-q$ & $-q$ are placed at A & C
Where $2q$ on B
So length of $A=d$

So the dipole moment

$p=(q\times d)$

So, Resultant dipole moment
$P=\left[\right(qd{)}^2+(qd{)}^2+2qd\times qd\cos {60}^o{]}^{1/2}$

$=[3q^2{d}^2{]}^{1/2}=\sqrt{3}qd=\sqrt{3}P$.