NEET · Physics · STD 12 - 4. Moving charges and magnetism

A very long conducting wire is bent in a semicircular shape from \(A\) to \(B\) as shown in figure. The magnetic field at point \(P\) for steady current configuration is given by:

A \(\frac{\mu_0 i }{4 R }\left[1-\frac{2}{\pi}\right]\) pointed into the page
B \(\frac{\mu_0 i }{4 R }\) pointed into the page
C \(\frac{\mu_0 i }{4 R }\) pointed away from the page
D \(\frac{\mu_0 i }{4 R }\left[1-\frac{2}{\pi}\right]\) pointed away from page

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\mu_0 i }{4 R }\left[1-\frac{2}{\pi}\right]\) pointed away from page

Step-by-step Solution

Detailed explanation

\(B =\frac{\mu_0}{4 \pi} \frac{I}{R}(\pi)-\frac{\mu_0}{4 \pi} \frac{2 I }{ R }\) \(=\frac{\mu_0 I }{4 R }\left[1-\frac{2}{\pi}\right] \text { outward i.e away from page. }\)

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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