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Three points charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.
The potential at the centroid of the triangle is zero.
The dipole moment of the system is $\sqrt 3 \,qL$
The dipole moment of the system is $\sqrt 2 \,qL$
$A$ and $B$ both
Solution
For equilateral triangle $\mathrm{AOB}, A O=O B=B A=a$ and $A C=O C=B C=r$
The potential at centroid $\mathrm{C}$ is $V=k \frac{2 q}{A C}+k \frac{-q}{O C}+k \frac{-q}{B C}=k \frac{2 q}{r}-k \frac{q}{r}-k \frac{q}{r}=0$
The net electric field at centroid $\mathrm{C}$ is $E=k \frac{2 q}{r^{2}}-k \frac{q}{r^{2}} \cos 30-k \frac{q}{r^{2}} \cos 30=k(0.2) \frac{2 q}{r^{2}} \neq$ $0$
As the total charge is zero so for dipole moment the choice of origin is independent. we assume $O$ as origin.
dipole moment, $p=-q(0)-q(L \hat{i})+2 q\left(\frac{L}{2} \hat{i}+\frac{\sqrt{3} L}{2} \hat{j}\right)$
or $p=\sqrt{3} q L \hat{j}$
