समान लम्बाई \(l\) की दो लम्बी सम-अक्षीय परिनालिकाये हैं। आन्तरिक एवं बाह्य कुण्डलियों की त्रिज्यायें क्रमशः
\(r _{1}\) तथा \(r _{2}\) है और प्रति इकाई लम्बाई फेरों की संख्या क्रमश: \(n _{1}\) तथा \(n _{2}\) है। आन्तरिक कुण्डलों के अन्योन्य प्रेरकत्व तथा स्वप्रेकरत्व का अनुपात होगा।

A \(\frac{{{n_1}}}{{{n_2}}}\)
B \(\frac{{{n_2}}}{{{n_1}}}.\frac{{{r_1}}}{{{r_2}}}\)
C \(\frac{{{n_2}}}{{{n_1}}}.\frac{{r_2^2}}{{r_1^2}}\)
D \(\frac{{{n_2}}}{{{n_1}}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{{{n_2}}}{{{n_1}}}\)

Step-by-step Solution

Detailed explanation

\(\ \frac{M}{L} =\frac{\mu_{0} n n_{1} n_{2} n_{1}^{2} \ell}{\mu_{0} \pi n_{1}^{2} r_{1}^{2} \ell}\) \(=\frac{n_{2}}{n_{1}}\)

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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