Question

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

• A. $\sqrt{3}ql\frac{\hat{j}-\hat{i}}{\sqrt{2}}$
• B. $2ql\hat{j}$
• C. $-\sqrt{3}ql\hat{j}$
• D. $\left(ql\right)\frac{\hat{j}-\hat{i}}{\sqrt{2}}$

Answer 1

The correct option is C $-\sqrt{3}ql\hat{j}$


Dipole moment is given by,

$P=\text{charge}\times \text{distance between two charges}$
So for two pairs of dipoles we can write,

$|P_1|=q\left(l\right)$

$|P_2|=q\left(l\right)$

$|\text{Resultant}|=2P\cos {30}^{\circ }$

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

So, ${\overrightarrow{P}}_{\text{Resultant}}=-\sqrt{3}ql\hat{j}$

As the resultant is along negative y-axis direction.