Question

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

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

Answer 1

The correct option is B $\sqrt{3}Qa$

$|\overrightarrow{P_1}|=Qa,|\overrightarrow{P_2}|=Qa$
And they are at ${60}^{\circ }$ inclination.
$\therefore P_{net}=\sqrt{P_1^2+P_2^2+2P_1{P}_{2}cos\theta }$
$=\sqrt{Q^2{a}^2+Q^2{a}^2+2Q^2{a}^2.\frac{1}{2}}$
$=\sqrt{3}Qa$.