Question

A bar magnet of magnetic moment \(M\) is cut into two parts symmetrically, perpendicular to its length. Then magnetic moment of each part is:

• A. \(M\)
• B. \(\dfrac{M}{2}\)
• C. \(2M\)
• D. \(\dfrac{M}{4}\)

Hint:

• Cutting magnet perpendicular to length \(\rightarrow\) magnetic moment halves.
• Cutting magnet parallel to length \(\rightarrow\) pole strength halves.

Answer 1

The Correct Option is B

Concept: Magnetic moment of a bar magnet is given by: \[ M = m(2l) \] where:

• \(m\) = pole strength
• \(2l\) = magnetic length of the magnet

When a magnet is cut perpendicular to its length:

• Pole strength remains unchanged
• Length becomes half

Therefore, magnetic moment becomes half.

Step 1: Write the formula for magnetic moment.
Magnetic moment is: \[ M = m(2l) \] where magnetic moment depends directly on magnetic length.

Step 2: Understand the effect of cutting perpendicular to length.
When the magnet is cut perpendicular to its length: \[ 2l \rightarrow l \] Thus, new length becomes half. However, cross-sectional area remains same, so pole strength remains unchanged. \[ m = \text{constant} \]

Step 3: Calculate the new magnetic moment.
New magnetic moment: \[ M' = m(l) \] But, \[ M = m(2l) \] Therefore, \[ M' = \frac{M}{2} \] Hence, magnetic moment of each part is: \[ \boxed{\frac{M}{2}} \]