The mutual inductance of two coaxial coils is \( 2\,\mathrm{H} \). The current in one coil is changed uniformly from zero to \( 0.5\,\mathrm{A} \) in a time of \( 100\,\mathrm{ms} \). The induced emf in the other coil during the change is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( -10\,\mathrm{V} \)
In mutual induction, the emf induced in one coil is proportional to the rate of change of current in the other, \( \varepsilon_2 = -M\,dI_1/dt \). The change is uniform, so the rate is \( \Delta I/\Delta t \).
\( \Delta I = 0.5\,\mathrm{A} - 0 = 0.5\,\mathrm{A} \)
\( \Delta t = 100\,\mathrm{ms} = 0.1\,\mathrm{s} \)
\( \displaystyle \varepsilon_2 = -M\,\frac{\Delta I}{\Delta t} = -2\,\mathrm{H}\times\frac{0.5\,\mathrm{A}}{0.1\,\mathrm{s}} = -10\,\mathrm{V} \)
The negative sign expresses Lenz’s law: the induced emf opposes the growth of current in the first coil.