એક વર્તુળાકાર વાહક લૂપને \(0.4\,T\) મૂલ્યના સમાન ચુંબકીય ક્ષેત્રમાં ક્ષેત્રને લંબ સમતલમાં મૂકેલી છે. કોઇક કારણસર \(1\,mm / s\) ના અચળ દરે વિસ્તારણ શરૂ થાય છે. જ્યારે લૂપની ત્રિજ્યા \(2\,cm\) થાય તે વખતે લૂપમાં પ્રેરિત થતા \(emf\) નું મૂલ્ય \(........\,\mu V\) હશે.

A \(40\)
B \(30\)
C \(20\)
D \(50\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(50\)

Step-by-step Solution

Detailed explanation

\(\frac{ dr }{ dt }=10^{-3}\,m / s\) \(\frac{ dA }{ dt }=2 \pi r \frac{ dr }{ dt }\) \(\varepsilon=\left|\frac{- d \phi}{ dt }\right|=\left|\frac{ BdA }{ dt }\right|\) \(=0.4 \times 2 \times \pi \times 2 \times 10^{-2} \times 10^{-3}\,V\) \(=16 \pi\, \mu V =50.24\,\mu V\)

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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