Q 12-01-147JEE MainJEE Main 2019 (12 Jan, Shift 1)Easy
Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:
Answer: (B) $-\sqrt3\,ql\,\hat{j}$
The total charge is zero, so $\vec{p} = \sum q_i\vec{r}_i$ is independent of origin. With $+q$ at $(0, 0)$, $+q$ at $(l, 0)$ and $-2q$ at $\left(\dfrac l2, \dfrac{\sqrt3l}{2}\right)$:
$$\vec{p} = q(l\hat{i}) - 2q\left(\frac l2\hat{i} + \frac{\sqrt3l}{2}\hat{j}\right) = -\sqrt3\,ql\,\hat{j}$$
Solution by Sreeraj P, M.Sc Physics