Three point charges + q, + q and -2q are placed at the corner of an equilateral triangle of side 'a'. The net dipole moment of the system is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $qa\sqrt{3}$
Place charges at A:(0,0) with +q, B:(a,0) with +q, and C:$(\frac{a}{2},\frac{\sqrt{3}}{2}a)$ with −2q.
Dipole moment $\mathbf{p}=\sum q_i\mathbf{r}_i = q\mathbf{r}_A + q\mathbf{r}_B -2q\mathbf{r}_C$.
$\mathbf{r}_A+\mathbf{r}_B=(a,0),\quad 2\mathbf{r}_C=(a,\sqrt{3}a)$
Hence $\mathbf{p}=q\big((a,0)-(a,\sqrt{3}a)\big)=q(0,-\sqrt{3}a)$
Magnitude: $p = q\sqrt{3}\,a$. Direction: along the altitude from the −2q charge toward the midpoint of the side joining the two +q charges (i.e. downward in the chosen coordinates).