If the magnetic flux through each turn of the coil consisting of 200 turns is (t² - 3t) milli-Webers, where t is in seconds, then the induced emf in the coil at t = 4 sec is

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