Question

Three point charges of 2q, -q and -q are placed at the corner of an equilateral triangle of side a. Then:

• A. the potential at the centroid of the triangle is zero
• B. the electric field at the centroid of triangle is zero
• C. the dipole moment of the system is $\sqrt{2}qa\hat{j}$
• D. the dipole moment of the system is $\sqrt{3}qa\hat{j}$

Answer 1

Answer: (A), (D)

The correct options are
A the potential at the centroid of the triangle is zero
D the dipole moment of the system is $\sqrt{3}qa\hat{j}$

Since the triangle is equilateral, the vertices are at equal distance from the centroid $h$ as shown in the figure.

Thus, the potential at centroid is $V=\frac{2q}{4\pi {ϵ}_{0}h}+\frac{-q}{4\pi {ϵ}_{0}h}+\frac{-q}{4\pi {ϵ}_{0}h}=0$

Thus, potential at centroid is zero.

The dipole moment of a neutral distribution of charges is given by

$\overrightarrow{p}=\sum q_i\overrightarrow{r_i}=(-q)(-\frac{L}{2}\hat{i})+(-q)\left(\frac{L}{2}\hat{i}\right)+\left(2q\right)\left(\frac{\sqrt{3}L}{2}\hat{j}\right)=\sqrt{3}qL\hat{j}$