Mutual Inductance

NCERT Class 12, Chapter 6 (Electromagnetic Induction) defines mutual inductance $M$ through the relation ${\epsilon }_2=-M\frac{d{I}_1}{dt}$, meaning the emf induced in a secondary coil is proportional to the rate of change of current in the primary. Rearranging for magnitude gives $M=\frac{{\epsilon }_2}{d{I}_1/dt}=\frac{0.15}{5}=0.03\text{H}=30\text{mH}$. The option 75 mH incorrectly multiplies rather than divides the two quantities. The option 0.75 mH misplaces the decimal by a factor of forty. The option 3.0 mH divides by an extra factor of ten. As a plausibility check, the units work out as volts divided by (amperes per second) equals volt-seconds per ampere, which is precisely the henry, and a value of tens of millihenries is realistic for closely coupled laboratory coils. Mutual inductance depends only on the geometry and relative orientation of the two coils, not on the currents themselves.