The magnetic field in the illustrated cylindrical region 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 . What is the current (magnitude and direction) in the wire ad if switch S₁ is open while S₂ is closed?

Step-by-step solution

Since switch S₁ is open and S₂ is closed, no current can flow through the left loop defa . The only closed circuit is the right square loop abcd . The area of the square loop abcd is: A = (1.00 cm )^2 = (1.00 10⁻² m )^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 the loop abcd is: = A dB dt = (1.00 10⁻⁴) (20.0 10⁻³) = 2.0 10⁻⁶ V The loop abcd consists of four sides ( ab , bc , cd , da ), each with a resis