Faraday's Law Of Induction

Question

A single circular loop of area 0.02 m^2 lies in a magnetic field that rises uniformly from 0.1 T to 0.5 T in 0.2 s. What is the magnitude of the average induced EMF in the loop?

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Faraday's law of electromagnetic induction states that the EMF induced in a closed loop equals the negative time rate of change of magnetic flux $\Phi = BA$ linking that loop. For a stationary loop of fixed area lying perpendicular to a changing field, only the field magnitude varies, so the flux change is governed entirely by $\Delta B$. The average induced EMF is $|\varepsilon| = A\,\dfrac{\Delta B}{\Delta t}$. Substituting $A = 0.02$ m^2, $\Delta B = 0.5 - 0.1 = 0.4$ T and $\Delta t = 0.2$ s gives $|\varepsilon| = 0.02 \times 0.4/0.2 = 0.04$ V. The option 0.02 V is wrong because it uses only half the field change. The option 0.08 V incorrectly doubles the area contribution. The option 0.20 V mistakenly drops the area factor and uses $\Delta B/\Delta t$ alone. This is the standard NCERT formulation of motional flux change in a fixed coil. A plausibility check confirms the unit T·m^2/s equals the volt, and the magnitude is reasonable for such a slow, weak-field variation.

Faraday's Law Of Induction

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