In the cylindrical region depicted, the magnetic field increases at a constant rate of 20.0 mT/s . Each side of the square loops abcd and defa has a length of 1.00 cm and a resistance of 4.00 . Find the current in the wire ad if both switches S₁ and S₂ are closed.

Step-by-step solution

Let us analyze the induced EMF and currents in the two square loops, defa (left loop) and abcd (right loop). The area of each square loop is: A = (1.00 cm )^2 = 1.00 10⁻⁴ m ^2 The rate of change of the magnetic field is: dB dt = 20.0 mT/s = 20.0 10⁻³ T/s According to Faraday's law of induction, the induced EMF in each loop is: = A dB dt = (1.00 10⁻⁴) (20.0 10⁻³) = 2.00 10⁻⁶ V Since the magnetic field is directed into the page and is increasing, Lenz's law states that the induced current will oppose this change by c