First slide

Magnetic flux and induced emf

Question

A circular coil of wire consists of exactly 100 turns with a total resistance of 0.20 $Ω$ . The area of the coils is 100 cm². The coil is kept in a uniform magnetic field B as
shown in the figure. The magnetic field is increased at a constant rate of 2 T/s. The induced current in the coil in A is _________.

Moderate

Solution

The total Faraday's flux through N turns of the coil
$i.e. ϕ_{total} = N B A \cos θ$
According to Faraday's law of electromagnetic induction,
we get
$E_{induced} = - \frac{d ϕ}{d t} = - \frac{d}{d t} [N B A \cos θ] = - N A \cos θ \frac{d B}{d t}$
$∴$ The current induced in the coil,
$I_{induced} = \frac{E_{induced}}{R} = \frac{100 \times 100 \times 10^{- 4} \times \cos 60^{\circ} \times 2}{0.2} = 5 A$

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