A circular coil of wire consists of exactly $$100$$ turns with a total resistance $$0.20$$Ω. The area of the coil is $$100$$ $$cm2$$. The coil is kept in a uniform magnetic field B as shown in figure. The magnetic field is increased at a constant rate of $$2$$ T $$s-1$$. Find the induced current in the coil in A.

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The total flux through N turns of the coil,

$ϕ_{total} = NBAcosθ$

According to Faraday's law of electromagnetic induction,

$E_{induced} = - \frac{dϕ}{dt} = - \frac{d}{dt} (NBAcosθ) = - (NAcosθ) \frac{dB}{dt}$

The current induced in the coil,

$I_{induced} = \frac{E_{induced}}{R} = 5 A$

Magnetic flux and induced emf

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A circular coil of wire consists of exactly 100 turns with a total resistance 0.20 $Ω$ . The area of the coil is 100 cm². The coil is kept in a uniform magnetic field B as shown in figure. The magnetic field is increased at a constant rate of 2 T s^-1. Find the induced current in the coil in A.

The total flux through N turns of the coil,
$ϕ_{total} = NBAcosθ$
According to Faraday's law of electromagnetic induction,
$E_{induced} = - \frac{dϕ}{dt} = - \frac{d}{dt} (NBAcosθ) = - (NAcosθ) \frac{dB}{dt}$
The current induced in the coil,
$I_{induced} = \frac{E_{induced}}{R} = 5 A$

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