Correct Answer - Option 1 : -1 V
Concept:
According to Faraday's law, the induced emf in a coil (having N turns) is the rate of change of magnetic flux linked with coil,
\({\rm{e}} = {\rm{-N}}\frac{{{\rm{d}}ϕ }}{{{\rm{dt}}}}\)
N = number of turns in the coil
ϕ = magnetic flux link with the coil
Calculation:
Given that ϕ = (t2 – 3t) m-wb and N = 200
Induced emf in coil
\({\rm{e}} = {\rm{-N}}\frac{{{\rm{d}}ϕ }}{{{\rm{dt}}}}\)
\({\rm{e}} = -200\frac{{\rm{d}}}{{{\rm{dt}}}}\left( {{{\rm{t}}^2} - 3{\rm{t}}} \right)×10^{-3}\)
e = -200 (2t - 3) × 10-3
then the induced emf in the coil at t = 4
e = - 200 (2 × 4 - 3) × 10-3 = - 1 V