The magnetic flux linked with a coil at any instant t is given by \( \phi = (4t^{3} - 3t^{2} + 2t + 5)\,\mathrm{Wb} \). The emf induced in the coil at \( t = 3\,\mathrm{s} \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( -92\,\mathrm{V} \)
By Faraday's law the induced emf is the negative of the rate of change of flux; the negative sign is Lenz's law.
\( \displaystyle \varepsilon = -\frac{d\phi}{dt} = -(12t^{2} - 6t + 2) \)
At \( t = 3\,\mathrm{s} \):
\( \displaystyle \varepsilon = -(12 \times 9 - 6 \times 3 + 2) = -(108 - 18 + 2) = -92\,\mathrm{V} \)