A small circular wire loop is being used to measure changes in the magnetic field of an MRI machine. The current in the loop is used to measure the rate of change of the field as the magnet is turned on.

The loop is in the x-y plane and the magnetic field is in the z-direction (positive or negative, to be determined). The radius of the loop is r = 0.4 meters and the resistance of the loop is R = 0.2 Ohms. The loop is entirely within the magnetic field and the magnetic field is uniform (the same) everywhere in the loop.

Initially, the magnetic field is zero and, when turned on, increases at a constant rate for some time T. During this time, the current in the loop is i = 0.6 Amps counter-clockwise.

What is the magnitude and direction of the MRI's magnetic field at a time t = 3.0 sec after the field is first turned on? The answer should be positive for a field in the +z direction and negative for a field in the -z direction. You can assume that t