સમાન લંબાઈ \(l\) ના બે લાંબા સમકેન્દ્રીય સોલેનોઇડ છે. ક્રમશઃ અંદર અને બહારનાં ગુંચળાની ત્રિજ્યા \(r_1\) અને \(r_2\) અને પ્રતિ એકમ લંબાઈ આંટાવોની સંખ્યા \(n_1\) અને \(n_2\) છે. અંદરના ગુંચળાનો અન્યોન્ય પ્રેરણ થી આત્મપ્રેરણનું ગુણોત્તર _____ થાય.

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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