Question

A magnet of magnetic moment \(\mathrm{M}\) and pole strength \(\mathrm{m}\) is divided in two equal parts, then magnetic moment of each part will be (a) \(\mathrm{M}\) (b) \((\mathrm{M} / 2)\) (c) \((\mathrm{M} / 4)\) (d) \(2 \mathrm{M}\)

Short answer

The magnetic moment of each part of the divided magnet is (c) M/4.

Step-by-step solution

Understanding the definition of magnetic moment

The magnetic moment of a magnet is the product of its pole strength (m) and the distance (d) between its poles. Mathematically, it can be written as: \[M = m \cdot d\] Since the magnet is divided into two equal parts, the pole strength of each part will also be divided equally.

Analyzing the division of the magnet

When the magnet is divided into two equal parts, the length (distance between the poles) of each part will be half of the initial magnet's length. As the pole strengths of each half are also halved, we can represent these new values as: New pole strength (m') = m / 2 New distance between the poles (d') = d / 2

Calculating the magnetic moment of each part

We now have the new pole strength and distance values for the two equal parts of the magnet. Using the formula for the magnetic moment, we can calculate the magnetic moment of each half: New magnetic moment (M') = new pole strength (m') * new distance (d') Since m' = m / 2 and d' = d / 2, we can substitute these values into the equation: M' = (m / 2) * (d / 2) M' = (1/4) * m * d Since the original magnetic moment (M) = m * d, we can write the equation for the new magnetic moment as: M' = (1/4) * M

Conclusion

Finally, we find that the magnetic moment of each part of the divided magnet is: (c) M'/2 So, the correct answer is (c): M/4