Given: Magnetic flux (ϕ) = 5t^{2 }+ 3t + 16
induced emf = \(-\frac{d\phi}{dt}\)
\(\epsilon\)=\(\frac{d(5t^2+3t+16}{dt}\) =10t+3
Therefore induced e.m.f. , when t=3,
\(|\epsilon_3|=(10\times3)+3=33 V\)
induced e.m.f. , when t=4 ,
\(|\epsilon_4|=(10\times4)+3=43 V\)
Therefor e.m.f. induced in the fourth second
=\(|\epsilon_4|-|\epsilon_3|=43-33=10V\)