The magnetic flux passing perpendicular to the plane of coil is changing according to the equation \( \Phi = 6t^{2} + 7t + 1 \), where '\( \Phi \)' is in mWb and 't' in sec. The magnitude of induced emf at t = 2s is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 31 mV
By Faraday's law the magnitude of the induced emf is the rate of change of magnetic flux at that instant.
\( \displaystyle \varepsilon = \frac{d\Phi}{dt} = \frac{d}{dt}\left(6t^{2} + 7t + 1\right) = 12t + 7 \)
With \( \Phi \) in mWb and \( t \) in s, the emf is in mV. At \( t = 2\,\mathrm{s} \):
\( \varepsilon = 12 \times 2 + 7 = 31\,\mathrm{mV} \)