त्रिज्या \(a\) के किसी लम्बे सीधे तार से कोई स्थायी धारा प्रवाहित हो रही है। इस तार की अनुप्रस्थ काट पर धारा एकसमान रूप से वितरित है । तार के अक्ष से त्रिज्य दूरियों \(\frac{ a }{2}, 2 a\) पर क्रमशः चुम्बकीय क्षेत्रों \(B\) और \(B'\) का अनुपात है।

A \(\frac{1}{2}\)
B \(1\)
C \(4\)
D \(\;\frac{1}{4}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1\)

Step-by-step Solution

Detailed explanation

Magnetic field at a point inside the wire at distance \(r\left(=\frac{a}{2}\right)\) from the axis of wire is \(B=\frac{\mu_{0} I}{2 \pi a^{2}} r=\frac{\mu_{0} I}{2 \pi a^{2}} \times \frac{a}{2}=\frac{\mu_{0} I}{4 \pi a}\)

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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