A circular coil of 200 turns and radius 0.05 m is placed perpendicular to a uniform magnetic field. The magnetic field is decreased uniformly from 0.80 T to 0.20 T in 0.10 s. What is the magnitude of the induced emf in the coil? (Use π = 3.14)

Correct answer

C. 9.42 V

Principle or equation

Faraday's law of induction: the induced emf is the negative rate of change of magnetic flux through the coil. For a coil of N turns, ε = N |ΔΦ/Δt|, where Φ = BA cos θ and θ is the angle between the magnetic field and the normal to the coil. Here θ = 0°, so Φ = BA.

Why this answer is correct

The area of the coil is A = πr² = 3.14 × (0.05)² = 7.85 × 10⁻³ m². The initial flux is Φ_i = B_i A = 0.80 × 7.85 × 10⁻³ = 6.28 × 10⁻³ Wb. The final flux is Φ_f = B_f A = 0.20 × 7.85 × 10⁻³ = 1.57 × 10⁻³ Wb. The change in flux is ΔΦ = Φ_f - Φ_i = -4.71 × 10⁻³ Wb. The magnitude of the induced emf is ε = N |ΔΦ/Δt| = 200 × (4.71 × 10⁻³ / 0.10) = 200 × 0.0471 = 9.42 V.

Example

If a single loop (N=1) with area 0.01 m² has its magnetic field change from 0.5 T to 0.1 T in 0.2 s, the induced emf is |ΔΦ/Δt| = (0.4 × 0.01)/0.2 = 0.02 V.