A loop with N = 2 turns and area 0.05 m^2 experiences a magnetic field increasing from 0 to 0.20 T in 0.10 s. What is the induced emf magnitude?

A loop with N = 2 turns and area 0.05 m^2 experiences a magnetic field increasing from 0 to 0.20 T in 0.10 s. What is the induced emf magnitude?

• A. 0.20 V
• B. 0.10 V
• C. 0.05 V
• D. 0.40 V

Answer: (A)

When a magnetic field through a loop changes, an electromotive force is induced according to Faraday’s law. The induced emf magnitude is ε = N |dΦ/dt|, where Φ = B A if the field is perpendicular to the loop. Here, the area is 0.05 m^2 and the field rises from 0 to 0.20 T, so the change in flux is ΔΦ = A ΔB = 0.05 × 0.20 = 0.01 Wb. This change happens over 0.10 s, giving dΦ/dt = 0.01 / 0.10 = 0.10 Wb/s. With N = 2 turns, the induced emf magnitude is ε = 2 × 0.10 = 0.20 V. The negative sign would indicate direction, but the magnitude is 0.20 V.

When a magnetic field through a loop changes, an electromotive force is induced according to Faraday’s law. The induced emf magnitude is ε = N |dΦ/dt|, where Φ = B A if the field is perpendicular to the loop.

Here, the area is 0.05 m^2 and the field rises from 0 to 0.20 T, so the change in flux is ΔΦ = A ΔB = 0.05 × 0.20 = 0.01 Wb. This change happens over 0.10 s, giving dΦ/dt = 0.01 / 0.10 = 0.10 Wb/s.

With N = 2 turns, the induced emf magnitude is ε = 2 × 0.10 = 0.20 V. The negative sign would indicate direction, but the magnitude is 0.20 V.