Question

Magnetic moment of a thin bar magnet is ‘M’. If it is bent into a semicircular form, its new magnetic moment will be________.
Fill in the blank with the correct answer from the options given below.

• A. \(\frac {M}{π}\)
• B. \(\frac M2\)
• C. \(\frac {2M}{π}\)
• D. \(M\)

Answer 1

The Correct Option is C

To determine the new magnetic moment of a thin bar magnet reshaped into a semicircle, we examine how the magnetic moment is altered by this geometrical change. The magnetic moment (\(M\)) of a straight bar magnet is defined as the product of its pole strength (\(m\)) and its length (\(l\)): \(M = m \cdot l\).

When the magnet is bent into a semicircle, its pole strength remains constant. However, the effective length of the magnet is now represented by the chord connecting the two ends of the semicircle. The arc length of the semicircle is equal to the original length (\(l\)) of the straight magnet. The radius (\(r\)) of this semicircle can be found using the relationship \(r = \frac{l}{\pi}\), derived from the arc length formula \(l = \pi r\).

Consequently, the direct linear distance between the magnet's poles, which is the chord length, becomes the diameter of the semicircle. This diameter is calculated as \(2r = \frac{2l}{\pi}\). The revised magnetic moment (\(M'\)) is then calculated as:

\(M' = m \cdot \text{chord length} = m \cdot \frac{2l}{\pi}\).

Given that the original magnetic moment was \(M = m \cdot l\), the new magnetic moment, expressed in terms of \(M\), is:

\(M' = \frac{2M}{\pi}\).

Therefore, the magnetic moment of the magnet after being bent into a semicircular form is \(\frac{2M}{\pi}\).