Determine the electric dipole moment of the system of three charges, placed on the vertices of an…

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

1. $\sqrt{3}ql\frac{\widehat{j}-\widehat{i}}{\sqrt{2}}$
2. $-\sqrt{3}ql\widehat{j}$
3. $2\mathrm{ }ql\mathrm{ }\mathrm{ }\widehat{j}$
4. $\left(ql\right)\frac{\widehat{i}+\widehat{j}}{\sqrt{2}}$

Solution

$\left|{\overrightarrow{P}}_1\right|=q\mathcal{l}$

$\left|{\overrightarrow{P}}_2\right|=q\mathcal{l}$



Angle between them ${60}^{\mathrm{o}}$

$\therefore$ Resultant dipole moment $P=\sqrt{{\left(ql\right)}^2+{\left(ql\right)}^2+2{\left(ql\right)}^2\cos {60}^{\mathrm{o}}}$

$=\sqrt{3}$ $\text{ql}$

As $\left|{\overrightarrow{P}}_1\right|=\left|{\overrightarrow{P}}_2\right|$ direction of resultant is along negative y axis thus option is $-\sqrt{3}ql\widehat{j}$

Asked in: JEE Main 2019 (12 Jan Shift 1)

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