\(\mathrm{r}\) त्रिज्या के एक वृत्ताकार पाश में \(\mathrm{IA}\) धारा बहती है। वृत्ताकार पाश के केन्द्र तथा इसकी अक्ष पर पाश के केन्द्र से \(\mathrm{r}\) दूरी पर चुम्बकीय क्षेत्र का अनुपात है:

A \(1: 3 \sqrt{2}\)
B \(3 \sqrt{2}: 2\)
C \(2 \sqrt{2}: 1\)
D \(1: \sqrt{2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(2 \sqrt{2}: 1\)

Step-by-step Solution

Detailed explanation

Magnetic field due to current carrying circular loop on its axis is given as \(\frac{\mu_0 ir ^2}{2\left( r ^2+ x ^2\right)^{3 / 2}}\) At centre, \(x=0, B_1=\frac{\mu_0 i }{2 r }\) At \(x=r, B_2=\frac{\mu_0 i}{2 \times 2 \sqrt{2 r}}\) \(\frac{ B _1}{ B _2}=2 \sqrt{2}\)

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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