A square coil with 120 turns and side length 0.10 m is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnetic field is reduced uniformly from 0.60 T to 0.10 T in 0.30 s. What is the magnitude of the average induced emf in the coil?

Correct answer

C. 2.0 V

Principle or equation

Faraday's law of induction states that the induced emf is equal to the negative rate of change of magnetic flux through the coil. For a coil of N turns, the magnitude is |emf| = N |ΔΦ/Δt|, where Φ = BA for a field perpendicular to the coil area.

Why this answer is correct

The area of the coil is A = (0.10 m)^2 = 0.010 m^2. The change in magnetic flux is ΔΦ = A ΔB = 0.010 m^2 × (0.10 T - 0.60 T) = -0.0050 Wb. The magnitude of the change is 0.0050 Wb. The time interval is 0.30 s. The induced emf magnitude is |emf| = N |ΔΦ|/Δt = 120 × 0.0050 Wb / 0.30 s = 2.0 V.

Example

If a coil of 50 turns and area 0.020 m^2 has its perpendicular magnetic field changed from 0.10 T to 0.50 T in 0.20 s, the induced emf is 50 × 0.020 × 0.40 / 0.20 = 2.0 V.