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Electromagnetic Induction

Question

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The magnetic flux linked with a coil at any instant t is given by the equation $ϕ = 5 t^{3} - 100 t + 300$ . The magitude of emf induced in coil after 3 s is

10 V

20 V

35 V

70 V

Solution

C.

35 V

Given:- $ϕ = 5 t^{3} - 100 t + 300$

$e = - \frac{dϕ}{dt}$

= $- \frac{d}{dt} (5 t^{3} - 100 t + 300)$

= $- (15 t^{2} - 100 + 0)$

= 15 t² + 100

$∴ \frac{e}{t} = - 15 {(3)}^{2} + 100$

= -135 + 100

$\Rightarrow \frac{e}{t} = - 35 V$

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