A circular coil of 100 turns and radius 0.10 m is placed perpendicular to a uniform magnetic field. The magnetic field is increased uniformly from 0.20 T to 0.60 T in 0.20 s. What is the magnitude of the induced emf in the coil? (Use π ≈ 3.14)

Correct answer

C. 6.28 V

Principle or equation

Faraday's law: induced emf ε = -N ΔΦ/Δt, where Φ = BA for a coil perpendicular to the field.

Why this answer is correct

Area A = πr² = 3.14 × (0.10)² = 0.0314 m². ΔB = 0.60 - 0.20 = 0.40 T. ΔΦ = A ΔB = 0.0314 × 0.40 = 0.01256 Wb. Δt = 0.20 s. ε = N ΔΦ/Δt = 100 × 0.01256 / 0.20 = 100 × 0.0628 = 6.28 V.

Example

For a single loop of area 0.01 m² with ΔB = 0.5 T in 0.1 s, ε = 1 × 0.01 × 0.5 / 0.1 = 0.05 V.