\(8.0 \,{cm}\) ત્રિજ્યા અને \(20\) આંટા ધરાવતી વર્તુળાકાર ગુચળું એકસમાન \(3.0 \times 10^{-2}\, {T}\) જેટલા સમક્ષિતિજ ચુંબકીયક્ષેત્રમાં તેના શિરોલંબ વ્યાસને અનુલક્ષીને \(50\, {rad} {s}^{-1}\) ની કોણીય ઝડપથી ભ્રમણ કરે છે. ગૂચાળામાં પ્રેરિત થતો મહત્તમ \(emf\) \(\ldots \ldots \times 10^{-2}\;volt\) જેટલો હશે. (નજીકના પૂર્ણાંકમાં)

A \(140\)
B \(40\)
C \(60\)
D \(650\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(60\)

Step-by-step Solution

Detailed explanation

Maximum emf \(\varepsilon={N} \omega {AB}\) \({N}=20, \omega=50, {B}=3 \times 10^{-2} {T}\) \(\varepsilon=20 \times 50 \times \pi \times(0.08)^{2} \times 3 \times 10^{-2}=60.28 \times 10^{-2}\) Rounded off to nearest integer \(=60\)

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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