A rectangular coil of 50 turns and area 0.020 m² is placed perpendicular to a uniform magnetic field. The magnetic field is increased uniformly from 0.10 T to 0.50 T in 0.20 s. What is the magnitude of the induced emf in the coil?
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Correct answer
C. 2.0 V
Principle or equation
Faraday's law: induced emf magnitude |ε| = N |ΔΦ/Δt|, where Φ = BA cosθ. Here θ = 0°, so ΔΦ = A ΔB.
Why this answer is correct
ΔB = 0.50 - 0.10 = 0.40 T. ΔΦ = A ΔB = 0.020 × 0.40 = 8.0 × 10⁻³ Wb. |ε| = N ΔΦ/Δt = 50 × (8.0 × 10⁻³)/0.20 = 50 × 0.040 = 2.0 V.
Example
If a 100-turn coil of area 0.01 m² has its perpendicular field change from 0.2 T to 0.6 T in 0.1 s, then |ε| = 100 × (0.01 × 0.4)/0.1 = 4 V.
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