Faraday's law of Electromagnetic induction

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Question

Magnetic flux $ϕ$ (in weber) linked with a closed circuit of resistance 10 ohm varies with time / (in seconds) as $ϕ = 5 t^{2} - 4 t + 1$ The induced electromotive force in the circuit at t = 0.2s is

Moderate

Solution

$e = - \frac{dϕ}{dt} = - (10 t - 4)$
$\Rightarrow {(e)}_{t = 0 .2 s} = - (10 \times 0 .2 - 4) = 2 volts$

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