As depicted in the figure, the magnetic field in the cylindrical region increases at a constant rate of 20.0 mT/s . Each side of the square loops abcd and defa possesses a length of 1.00 cm and a resistance of 4.00 . Determine the magnitude and direction of the current in the wire ad when the switch S₁ is closed and S₂ is open.

Step-by-step solution

When switch S₁ is closed and S₂ is open, the loop defa forms a closed circuit, while the loop abcd remains open. Therefore, induced current will only flow in the loop defa . The area of the square loop defa is: A = l^2 = (1.00 10⁻² m )^2 = 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 defa is: = A dB dt = (10⁻⁴ m ^2)(20.0 10⁻³ T/s ) = 2.0 10⁻⁶ V The loop defa consists of four sides ( de , ef , fa , ad ),