Question

Three charges are arranged at the vertices of an equilateral triangle of side $l$. The dipole moment of the combination is

• A. Zero
• B. $\sqrt{3}ql$
• C. $ql/\sqrt{3}$
• D. $\sqrt{2}ql$

Answer 1

The correct option is B $\sqrt{3}ql$

The components of ${\overrightarrow{P}}_1$ & ${\overrightarrow{P}}_2$ along the $x$ -axis will cancel out each other while the component along $y$ -axis will add up

$\left|{\overrightarrow{P}}_{net}\right|=\left[\left(ql\right)\cos {30}^{\circ }\right]\times 2$

$=\left(ql\right)\frac{\sqrt{3}}{2}\times 2$

$\left|{\overrightarrow{P}}_{net}\right|=\sqrt{3}ql$

Hence option (B) is correct