દરેક \(80 \mathrm{~cm}\) ની એવી ત્રણ બ્લેડ (પાંખીયા) ધરાવતો એક સીર્લીંગ ફેન (પંખો) \(1200 \mathrm{rpm}\) ના કોણીય વેગથી ભ્રમણ કરે છે. આ વિસ્તારમાં પૃથ્વીનું ચુંબકીય ક્ષેત્ર \(0.5 \mathrm{G}\) જેટલું છે અને ડીપ-કોણ \(30^{\circ}\) છે. પાંખીયાના છેડા વચ્ચે પ્રેરિત \(\mathrm{emf}\) \(N \pi \times 10^{-5} \mathrm{~V}\) મળે છે. \(N\) નું મૂલ્ય _______ છે.

A \(89\)
B \(32\)
C \(45\)
D \(27\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(32\)

Step-by-step Solution

Detailed explanation

\( B_v=B \sin 30=\frac{1}{4} \times 10^{-4} \) \( \omega=2 \pi \times f=\frac{2 \pi}{60} \times 1200 \mathrm{rad} / \mathrm{s} \) \( \varepsilon=\frac{1}{2} B_V \omega \ell^2 \) \( =32 \pi \times 10^{-5} \mathrm{~V}\)

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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