Question

Two identical thin bar magnets, each of length $l$ and pole strength $m$ are placed at right angles to each other with the north pole of one touching the south pole of the other. What is the resultant magnetic moment of the system?

• A. $ml$
• B. $\sqrt{2}ml$
• C. $\sqrt{3}ml$
• D. $\sqrt{5}ml$

Answer 1

The correct option is B $\sqrt{2}ml$


Let $M$ is the magnetic moment of each bar magnet, as $M=ml$.

The resultant magnetic moment,

$M_{res}=\sqrt{(M_1{)}^2+(M_2{)}^2+2M_1{M}_2\cos \theta }$

Since, the angle between the magnetic moments is ${90}^{\circ }$ as shown in figure.

$M_{res}=\sqrt{(M_1{)}^2+(M_2{)}^2}[\because M_1=M_2=M]$

$M_{res}=\sqrt{2}M=\sqrt{2}ml$

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