Q 12-05-006NEETEAMCET 2007 (Medical)Medium
A bar magnet of magnetic moment $M_1$ is axially cut into two equal parts. If these two pieces are arranged perpendicular to each other, the resultant magnetic moment is $M_2$. Then the value of $\dfrac{M_1}{M_2}$ is
Answer: (D) $\sqrt{2}$
Concept. Cutting a magnet along its axis halves the pole strength but keeps the length, so each piece has half the moment. Moments add as vectors.
Step 1. Moment of each piece. $\dfrac{M_1}{2}$.
Step 2. Combine at right angles.
$$M_2 = \sqrt{\left(\frac{M_1}{2}\right)^2 + \left(\frac{M_1}{2}\right)^2} = \frac{M_1}{\sqrt{2}}$$
Step 3. Ratio. $\dfrac{M_1}{M_2} = \sqrt{2}$.
Answer. $\sqrt{2}$ (Option D).
Solution by Sreeraj P, M.Sc Physics