Question: 36: The magnetic flux linked to a circular coil of radius R is :
\phi=2t^{3}+4t^{2}+2t+5\ \mathrm{Wb}The magnitude of induced emf in the coil at t=5\ \mathrm{s} is:
(1) 108 V
(2) 197 V
(3) 150 V
(4) 192 V
Answer: Option (4)
Explanation:
According to Faraday’s law of electromagnetic induction, the magnitude of induced emf in a coil is
given by \mathcal{E}=\left|\frac{d\phi}{dt}\right|.
The given magnetic flux is \phi=2t^{3}+4t^{2}+2t+5.
Differentiating with respect to time, we get \frac{d\phi}{dt}=6t^{2}+8t+2.
At time t=5\ \mathrm{s}, the induced emf is \mathcal{E}=6(5)^{2}+8(5)+2.
Calculating, \mathcal{E}=150+40+2=192\ \mathrm{V}.
Therefore, the magnitude of induced emf in the coil at
t=5\ \mathrm{s} is 192\ \mathrm{V},
and the correct option is (4).