Mutual Inductance

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Two coupled coils have a mutual inductance of 0.2 H. If the current in the primary coil changes steadily at the rate of 30 A/s, what EMF is induced in the secondary coil?

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Mutual inductance describes how a changing current in one coil drives an EMF in a neighbouring coil by linking part of its flux through the second winding, quantified by $\varepsilon_2 = -M\,\dfrac{dI_1}{dt}$. The magnitude of the secondary EMF therefore equals the mutual inductance multiplied by the rate at which the primary current changes. Substituting $M = 0.2$ H and $dI_1/dt = 30$ A/s gives $|\varepsilon_2| = 0.2 \times 30 = 6$ V. The option 3 V wrongly halves the rate of change. The option 0.6 V misplaces a decimal and effectively uses 3 A/s. The option 12 V doubles the mutual inductance. This is the coupling relation NCERT introduces using two concentric solenoids, where the same $M$ governs induction in either direction. A unit check confirms H·(A/s) reduces to volts, and a few volts is a realistic transformer-style coupling output for a modest current slew rate; the negative sign merely encodes Lenz's-law opposition and does not affect the magnitude requested.

Mutual Inductance

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