Question

Electric charge Q, Q and - 2 Q respectively are place at the three corner of an equilateral triangle of side a. Magnitude of the electric dipole moment of the system is:

Answer 1

Configuration of charges:

Imagine charges at $C(-2Q)$ be splited into charges of $(-Q)$ each so that $\left(AC\right)$ and $\left(BC\right)$ form two dipole systems.

Now, dipole moment:

$P_1=QA=p_2$

using vector addition

$|{\overrightarrow{P}}_{net}|=\sqrt{P_1^2+P_2^2+2P_1{P}_2\cos \theta }$ $[\theta ={60}^o]$

$p_{net}=QA\sqrt{3}$