\(R\) અવરોધ ધરાવતી ઉપવલય લૂપની અર્ધદીર્ધ અક્ષ \(a\) અને અર્ધલઘુ અક્ષ \(b\) ને ચુબકીયક્ષેત્રમાં મૂકેલી છે. જો લૂપને \(x-\) અક્ષને અનુલક્ષી ને \(\omega\) કોણીય આવૃતિથી ભ્રમણ કરાવતા જુલ અસરના કારણે લૂપમાં પાવર વ્યય

A \(\frac{\pi^{2} a ^{2} b ^{2} B ^{2} \omega^{2}}{2 R }\)
B Zero
C \(\frac{\pi^{2} a^{2} b^{2} B^{2} \omega^{2}}{R}\)
D \(\frac{\pi abB \omega}{ R }\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\pi^{2} a ^{2} b ^{2} B ^{2} \omega^{2}}{2 R }\)

Step-by-step Solution

Detailed explanation

\(\in= NAB \omega \cos \omega t \quad[ N =1]\) \(P _{ avg }=<\frac{\epsilon^{2}}{ R }>=<\frac{( AB \omega \cos \omega t )^{2}}{ R }>\) \(=\frac{ A ^{2} B ^{2} \omega^{2}}{ R } \frac{1}{2}=\frac{\pi^{2} a ^{2} b ^{2} B ^{2} \omega^{2}}{2 R }\)

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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