MHT CET · Physics · Magnetic Effects of Current

A steel wire of length ' \(\ell\) ' has a magnetic moment 'M'. It is then bent into a semicircular arc. The new magnetic moment is

A \(2 \mathrm{M} / \pi\)
B \(\mathrm{M}\)
C \(\mathrm{M} \times \ell\)
D \(\mathrm{M} / \ell\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \mathrm{M} / \pi\)

Step-by-step Solution

Detailed explanation

(C)
When wire is bent in the form of semicircular arc then, \(\mathrm{l}=\pi \mathrm{r}\) \(\therefore\) The radius of semicircular arc, \(\mathrm{r}=1 / \pi\)
Distance between two end points of semicircular wire \(=2 \mathrm{r}=\frac{21}{\pi}\) \(\therefore\) Magnetic moment of semicircular wire \(=m \times 2 r=m \times \frac{2 l}{\pi}=\frac{2}{\pi} m l\)
But \(\mathrm{ml}\) is the magnetic moment of straight wire i.e., \(\mathrm{ml}=\mathrm{M}\)
\(\therefore\) New magnetic moment \(=\frac{2}{\pi} \mathrm{M}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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