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Two magnets have the same length and th...

Two magnets have the same length and the same pole strenght . But one of the magnets have a small hole at its centre. Then

A

Both have equal magnetic moment

B

One with hole has smaller magnetic moment

C

One with hole has larger magnetic moment

D

One with hole loses magnetism through the hole

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the effect of having a hole in one of the magnets on its magnetic moment. ### Step-by-Step Solution: 1. **Understanding Magnetic Moment**: The magnetic moment (M) of a magnet is a measure of its strength and orientation in a magnetic field. It is given by the product of the pole strength (p) and the length (l) of the magnet. The formula is: \[ M = p \times l \] 2. **Comparing Two Magnets**: We have two magnets that are identical in length (L) and pole strength (p). Thus, for both magnets without any modifications, their magnetic moments would be the same: \[ M_1 = p \times L \quad \text{(for the first magnet)} \] \[ M_2 = p \times L \quad \text{(for the second magnet)} \] 3. **Effect of the Hole**: When one of the magnets has a small hole at its center, it effectively alters the distribution of the magnetic material. The presence of the hole means that there is a loss of magnetic material, which can lead to a reduction in the effective magnetic moment of that magnet. 4. **Magnetic Moment of the Magnet with a Hole**: The magnet with the hole will have a smaller effective magnetic moment because the hole reduces the amount of magnetic material contributing to the magnetic moment. Therefore, we denote the magnetic moment of the magnet with the hole as: \[ M_{hole} < M \] 5. **Conclusion**: Since the magnet with the hole has a reduced magnetic moment compared to the one without the hole, we can conclude that: - The magnet with the hole has a smaller magnetic moment. - The magnet with the hole also experiences losses in magnetism due to the hole. ### Final Answer: The correct option is that the magnet with the hole has a smaller magnetic moment and loses magnetism through the hole. ---
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