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

Each individual dipole vector has a magnitude of: $$p_1 = p_2 = ql$$

The two dipole vectors point from the top vertex downward toward the bottom-left and bottom-right vertices. Because the triangle is equilateral, the angle between these two vectors is $$60^\circ$$.

By symmetry, the horizontal components of these vectors cancel each other out, while their vertical components add together along the negative y-direction ($$-\hat{j}$$).

The net dipole moment ($$\vec{p}_{\text{net}}$$) is calculated by adding the vertical components:

$$\vec{p}_{\text{net}} = -\left(p_1 \cos 30^\circ + p_2 \cos 30^\circ\right)\hat{j}$$

$$\vec{p}_{\text{net}} = -\left(ql \frac{\sqrt{3}}{2} + ql \frac{\sqrt{3}}{2}\right)\hat{j} = -\sqrt{3}ql\hat{j}$$