Question

On dividing any magnet of magnetic moment \( M \) parallel to its length into \( n \) equal pieces, the moment of each piece will be:

• A. \( \frac{M}{n} \)
• B. \( \frac{n}{M} \)
• C. \( 2n \)
• D. \( M \times n \)

Hint:

Magnetic moment is directly proportional to the length of the magnet, so dividing length into \( n \) parts divides moment by \( n \).

Answer 1

The Correct Option is A

When a magnet with total magnetic moment \( M \) is divided into \( n \) equal parts parallel to its length, each piece behaves as a smaller magnet with a proportionally reduced magnetic moment. Since the magnetic moment is proportional to both the pole strength and the length of the magnet, dividing the magnet into \( n \) equal parts reduces the length of each piece to \( \frac{1}{n} \) of the original length while keeping the pole strength the same. Therefore, the magnetic moment of each piece is: \[ \text{Moment of each piece} = \frac{M}{n}. \] This means the total magnetic moment is conserved as the sum of the moments of all the pieces.