A single-turn loop of 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 single-turn loop of 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. 0.10 V
• B. 0.02 V
• C. 1.0 V
• D. 0.5 V

Answer: (A)

Faraday's law states that the induced emf equals the negative rate of change of magnetic flux through the loop. If the field is perpendicular to the loop, flux is Φ = B A. The loop area is 0.05 m^2, and B increases from 0 to 0.20 T, so the flux changes by ΔΦ = A ΔB = 0.05 × 0.20 = 0.01 Weber. This happens over Δt = 0.10 s, giving a rate of change dΦ/dt = 0.01 / 0.10 = 0.10 Weber per second. Therefore the induced emf magnitude is |ε| = |dΦ/dt| = 0.10 V. The negative sign in Faraday’s law would indicate the induced emf tries to oppose the increase in flux, but the magnitude is 0.10 volts.

Faraday's law states that the induced emf equals the negative rate of change of magnetic flux through the loop. If the field is perpendicular to the loop, flux is Φ = B A. The loop area is 0.05 m^2, and B increases from 0 to 0.20 T, so the flux changes by ΔΦ = A ΔB = 0.05 × 0.20 = 0.01 Weber. This happens over Δt = 0.10 s, giving a rate of change dΦ/dt = 0.01 / 0.10 = 0.10 Weber per second. Therefore the induced emf magnitude is |ε| = |dΦ/dt| = 0.10 V. The negative sign in Faraday’s law would indicate the induced emf tries to oppose the increase in flux, but the magnitude is 0.10 volts.