\(L\) બાજુ ધરાવતા તારના એક ચોરસ ગૂંચળાને \(L (L > > l)\) તારના બીજા મોટા ચોરસ ગૂંચળાની અંદર મૂકવામાં આવે છે. બંને ગાળાઓ એક જ સમતલમાં છે અને તેમના કેન્દ્રો આકૃતિમાં દર્શાવ્યા અનુસાર બિંદુ \(O\) આગળ સંપાત થાય છે. તંત્રનું અન્યોન્ય પ્રેરણ \(.........\) થશે.

A \(\frac{2 \sqrt{2} \mu_{0} L ^{2}}{\pi \ell}\)
B \(\frac{\mu_{0} \ell^{2}}{2 \sqrt{2 \pi L}}\)
C \(\frac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi L }\)
D \(\frac{\mu_{0} L ^{2}}{2 \sqrt{2} \pi \ell}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi L }\)

Step-by-step Solution

Detailed explanation

Assuming current I in outer loop magnetic field at \(\text { centre }=4 \times \frac{\mu_{0} i}{4 \pi \times \frac{L}{2}} \times\left(2 \sin 45^{\circ}\right)=\frac{2 \sqrt{2} \mu_{0} i}{\pi L }\) \(M =\frac{\text { Flux through inner loop }}{ i }\)…

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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