Question

Two identical thin bar magnets are placed mutually at right angles such that the north pole of one touches the south pole of the other. The length of each bar magnet is $\ell$. The magnitude of resultant magnetic moment of the system is
$\left[m = \text{pole strength of the magnet}\right]$

• A. $2m\ell$
• B. $\sqrt{2}\,m\ell$
• C. $m\ell$
• D. $\sqrt{3}\,m\ell$

Hint:

Magnetic moment is a vector quantity; use vector addition rules while combining them.

Answer 1

The Correct Option is B

Step 1: Magnetic moment of each bar magnet.
Magnetic moment of one bar magnet is given by:
\[ M = m\ell \]
Step 2: Orientation of magnetic moments.
The two magnetic moments are equal in magnitude and are placed mutually perpendicular to each other.

Step 3: Resultant magnetic moment.
For two vectors of equal magnitude $M$ at right angles, resultant is:
\[ M_R = \sqrt{M^2 + M^2} = \sqrt{2}\,M \]
Step 4: Substituting value of $M$.
\[ M_R = \sqrt{2}\,m\ell \]
Step 5: Conclusion.
The magnitude of resultant magnetic moment is $\sqrt{2}\,m\ell$.