Question

What is the net dipole moment for the given arrangement.

• A. $1.7\times {10}^{-2}Q$
• B. $1.7\times {10}^{-3}Q$
• C. $0.7Q$
• D. $Zero$

Answer 1

The correct option is A $1.7\times {10}^{-2}Q$

The arrangement can be seen as a two dipole system if we focus on equal and opposite charges. (as we know equal and opposite charges separated by fixed distance forms a dipole).


Each dipole has a charge +Q and separation of 0.01 m so $\left|\overrightarrow{P}\right|=0.01Q$ as the angle between them is ${60}^{\circ }$ the net dipole moment is $\left|\overrightarrow{P_{net}}\right|=$
$\sqrt{(0.01Q{)}^2+(0.01Q{)}^2+2\times 0.01Q\times 0.01Q\times \cos {60}^{\circ }}$
$=0.01\times \sqrt{3}Q.$
$=1.7\times {10}^{-2}Q$
As we can see from symmetry it will be directed in the positive y direction (mid way between the two vectors)