A conducting loop of area 0.50 m² is placed in a magnetic field that varies with time according to B(t) = 0.20t + 0.05 T, where t is in seconds. What is the magnitude of the induced emf in the loop at t = 4.0 s?

Core Concept

According to Faraday's law, the induced emf is equal to the negative rate of change of magnetic flux through the loop: ε = -dΦ/dt. For a uniform field perpendicular to the loop, Φ = BA, so ε = -A(dB/dt). Differentiating B(t) with respect to t gives dB/dt = 0.20 T/s. Therefore, ε = -(0.50 m²)(0.20 T/s) = -0.10 V. The magnitude of the induced emf is 0.10 V.