Question

Three point charges of $+2q$, $+2q$ and $-4q$ are placed at the corners $A$, $B$ and $C$ of an equilateral triangle $ABC$ of side '$x$'. The magnitude of the electric dipole moment of this system is :

• A. $2\sqrt{3}qx$
• B. $2qx$
• C. $3qx$
• D. $3\sqrt{2}qx$

Answer 1

Answer: (A)

$2\sqrt{3}qx$

The charge arrangement can be simplified as two dipoles, one on $CA$ and the other on $CB$.

Dipole moment on $CA=2qx$ in the direction of CA

Dipole moment on $CB=2qx$ in the direction of CB

Angle between them = ${60}^o$

Net dipole moment = Vector sum of both the dipole moments

Magnitude = $\sqrt{m_1^2+m_2^2+2m_1{m}_2\text{cos}\left({60}^o\right)}=\sqrt{3\times (2qx{)}^2}=2\sqrt{3}qx$