Question

If a magnet is cut into equal halves perpendicularly. What happens to magnetic moment?

• A. M
• B. $\frac{M}{2}$
• C. $\frac{M}{3}$
• D. $\frac{3M}{2}$

Hint:

- Cut perpendicular to axis: Length halves, pole strength is same $\implies M' = M/2$.
- Cut parallel to axis: Length is same, pole strength halves $\implies M' = M/2$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The magnetic moment (\(M\)) of a bar magnet is the product of its pole strength (\(m\)) and its magnetic length (\(2l\)).
Step 2: Key Formula or Approach:
\[ M = m \times 2l \]
When a magnet is cut, we must determine how its pole strength and length change.
Step 3: Detailed Explanation:
Let the initial magnetic moment be \(M = m \times 2l\), where '\(m\)' is the pole strength and '\(2l\)' is the total length.
When the magnet is cut into two equal halves perpendicularly (transversely to its magnetic axis):
- The pole strength (\(m\)) remains completely unchanged because the cross-sectional area of the poles is not altered.
- The new length of each half becomes half of the original length, so \(l_{new} = \frac{2l}{2} = l\).
Now, let's calculate the new magnetic moment (\(M'\)) for one of the halves:
\[ M' = \text{new pole strength} \times \text{new length} \]
\[ M' = m \times l \]
Since the original magnetic moment was \(M = m \times 2l \implies m = \frac{M}{2l}\).
Substituting this back:
\[ M' = \left(\frac{M}{2l}\right) \times l = \frac{M}{2} \]
Step 4: Final Answer:
The magnetic moment of each half becomes half of the original value, \(\frac{M}{2}\).