Question

What is the magnitude of dipole moment of the given charge arrangement

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

In this arrangement, pairs of equal and opposite charges form dipoles.

This arrangement has three dipoles with dipole moments shown

$\left|\overrightarrow{P_{net}}\right|=\sqrt{{\left|\overrightarrow{P_3}\right|}^2+{|\overrightarrow{P_1}+\overrightarrow{P_2}|}^2+2\left|\overrightarrow{P_3}\right||\overrightarrow{P_1}+\overrightarrow{P_2}|\cos {45}^{\circ }}$
$=\sqrt{(0.014{)}^2+(0.03{)}^2+2\times 0.014\times 0.03\times \frac{1}{\sqrt{2}}}$
$\approx 0.04Cm$
Since we are asked only the magnitude we can stop here.