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-20t 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

Question

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 = πr² = π(0.05)² m². The rate of change of B is dB/dt = -10e^(-20t) T/s. At t = 2.0 s, dB/dt = -10e^(-40) T/s. The induced emf is ε = A * |dB/dt|. The current I = ε/R = (A * |dB/dt|) / 0.20 Ω. Calculating gives approximately 2.6 mA.

A Circular Coil of Radius 5