First slide

Magnetic flux and induced emf

Question

The magnetic flux $ϕ$ through a coil varies with time t as shown in Fig.
Which graph shown in Fig. best represents the variation of induced emf e in the coil with time t.

Moderate

A
B
C
D

Solution

The graph shown in Fig. is a sine curve. Hence
$ϕ = ϕ_{0} \sin ωt = ϕ_{0} \sin (\frac{2 πt}{T})$
Induced emf is
$e = - \frac{dϕ}{dt} = - ϕ_{0} \times \frac{2 π}{T} \cos (\frac{2 πt}{T}) = - e_{0} \cos (\frac{2 πt}{T})$
It is clear that the correct choice is (4).

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