Faraday's law: A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = 0.50e^-20^t T. What is the magnitude of the current induced in the coil at the time t = 2.0 s? A) 1.3 mA B) 9.2 mA C) 7.5 mA D) 4.2 mA E) 2.6 mA

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Quizplus · Accepted Answer

The induced emf (ε) is given by Faraday's law: ε = -dΦ/dt, where Φ = B*A is the magnetic flux. The area A = π*(0.05 m)^2. At t = 2.0 s, B = 0.50e^(-40) T. The rate of change of B is dB/dt = -20*0.50e^(-40) T/s. Thus, ε = A*(-dB/dt). The current I = ε/R, where R = 0.20 Ω. Calculating gives I ≈ 2.6 mA.

Faraday's Law: a Circular Coil of Radius 5