Question

Electric charges $q,q$ and $-2q$ are placed at the corners of an equilateral triangle ABC of side $L$. The magnitude of electric dipole moment of the system is

• A. $qL$
• B. $2qL$
• C. $(\surd 3)qL$
• D. $4qL$

Answer 1

Answer: (C)

Electric dipole is a vector quantity

$\therefore$ Components along X-axis of $\overrightarrow{P}1$ and $\overrightarrow{P}2$ cancel out each other(opposite direction).

$\therefore$ Components along Y-axis will add up as:

$\mid {\overrightarrow{P}}_{ret}\mid =\left[\right(q\cdot L\left)\cos {30}^{\circ }\right]\times 2$

$=q\cdot L\cdot \frac{\sqrt{3}}{2}\times 2=\sqrt{3}qL$