Question

Three charges $q,q,-2q$ placed at the corners of equilateral triangle of side $l$ .Find the net dipole moment.

• A. 2q$l$
• B. $\sqrt{3}$q$l$
• C. $\frac{\sqrt{3}ql}{2}$
• D. $\frac{ql}{2}$

Answer 1

The correct option is B $\sqrt{3}$q$l$

From figure, we split $-2q$ charge into two $-q$ charges and calculate their dipole moment with $+q$ charges and then do the vector sum of two dipole moments to get the resultant dipole moment.

$p=q.l$

Angle between two dipole moments is ${60}^o$.

$p_{net}=\sqrt{p^2+p^2+2.p.p\cos {60}^o}$

$⟹p_{net}=\sqrt{3p^2}=p\sqrt{3}$

$⟹p_{net}=\sqrt{3}ql$

Answer-(B)