A circular loop of wire with radius 0.10 m is placed in a region where the magnetic field changes from 0.20 T to 0.80 T in 0.50 s. The loop has a resistance of 2.0 Ω. What is the magnitude of the induced current in the loop?

Core Concept

First, calculate the induced emf using Faraday's law: ε = -dΦ/dt. The magnetic flux through the loop is Φ = BA, where A = πr² = π(0.10 m)² = 0.0314 m². The change in flux is ΔΦ = AΔB = (0.0314 m²)(0.80 T - 0.20 T) = 0.0188 Wb. Therefore, ε = ΔΦ/Δt = 0.0188 Wb/0.50 s = 0.0376 V. Using Ohm's law, I = ε/R = 0.0376 V/2.0 Ω = 0.019 A.