Question

The magnetic flux linked with a coil, in webers, is given by the equations ∅=3t²+4t+9 . Then the magnitude of induced e.m.f. at t = 2 second will be(a) 2 volt(b) 4 volt(c) 8 volt(d) 16 volt

Answer 1

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According to Faradays law ,
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The induced emf produced in a closed path is equal to the rate of change of magnetic flux in the closed area.

i.e.

$= > e \: = \frac{d \phi \: }{dt}$

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Given
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$= > \phi = 3 {t}^{2} + 4t + 9$
Differentiating both sides we get
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$= > {\bf\frac{d \phi}{dt} }= \underline{6t + 4}$
Now .. by faradays law

=>Induced emf =
$\frac{d \phi}{dt} = 6t + 4$
at t = 2 second

=> Induced emf = 6(2) + 4 = 12+4= 16 volts

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