First slide

Faraday's law of Electromagnetic induction

Question

A 800 turn coil of effective area $0.05 m^{2}$ is kept perpendicular to a magnetic field $5 \times 10^{- 5} T$ . When the plane of the coil is rotated by $90 °$ around any of its coplanar axis in 0.1 s, the emf induced in the coil will be

Moderate

A

$0.02 V$
B

$2 V$
C

$0.2 V$
D

$2 \times 10^{- 3} V$

Solution

$Here N = 800, A = 0.05 m^{2} B = 5 \times 10^{- 5} T, Δt = 0.1 s Induced emf, ε = - \frac{Δϕ}{Δt} = - \frac{(ϕ_{f} - ϕ_{i})}{Δt} ϕ_{i} = N (\vec{B} \cdot \vec{A}) = 800 \times 5 \times 10^{- 5} \times 0.05 \times \cos 0 ° = 2 \times 10^{- 3} T m^{2} ϕ_{f} = 0 ∴ ε = \frac{- (0 - 2 \times 10^{- 3})}{0.1} = 2 \times 10^{- 2} V = 0.02 V$

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