Final answer:
The magnitude of the current induced in the circular coil cannot be determined without additional information about the rate of change of magnetic field with time. Faraday's law of electromagnetic induction can be used to calculate the induced emf and current in the coil.
Step-by-step explanation:
The magnitude of the current induced in the circular coil can be calculated using Faraday's law of electromagnetic induction. The induced emf (electromotive force) in the coil can be determined by multiplying the rate of change of magnetic field with time and the area of the coil. The induced current can then be calculated by dividing the induced emf by the resistance of the coil.
The given information states that the radius of the circular coil is 5.0 cm and the resistance is 0.20 ohms. However, the magnitude of the magnetic field changing over time (dB/dt) is not provided. Without this information, it is not possible to determine the magnitude of the current induced in the coil at t = 2.0 s. Further information is needed to solve the problem.