Question

Two positive charges $(+10\text{C})$ are kept on the arc of a circle and a negative charge $(-20\text{C})$ at the origin (centre of circle). Find the magnitude of net dipole moment for the given system.

• A. $89.3\text{C-m}$
• B. $59.3\text{C-m}$
• C. $69.3\text{C-m}$
• D. $79.3\text{C-m}$

Answer 1

The correct option is C $69.3\text{C-m}$

Here, assuming two negative charge of $10\text{C}$ each placed at the centre of the circle.


From formula, dipole moment $\overrightarrow{p}$ is
$\overrightarrow{p}=q\left(2\overrightarrow{l}\right)$

Now from figure,

$|\overrightarrow{p_1}|=10\times 4=40\text{C-m}$

and $|\overrightarrow{p_2}|=10\times 4=40\text{C-m}$

Angle between $\overrightarrow{p_1}$ and $\overrightarrow{p_2}$,

$\theta ={60}^{\circ }$

So,
$|{\overrightarrow{p}}_{\text{net}}|=\sqrt{p_1^2+p_2^2+2p_1{p}_2\cos \theta }$

$\Rightarrow |{\overrightarrow{p}}_{\text{net}}|=\sqrt{{40}^2+{40}^2+2\times 40\times 40\times \cos {60}^{\circ }}$

$\Rightarrow |{\overrightarrow{p}}_{\text{net}}|=69.3\text{C-m}$

Hence, option $\left(b\right)$ is the correct answer.