Question

The small rectangular loops sketched here are all moving upward at the same speed. The shaded region has a uniform magnetic field pointing out of the paper. The magnetic field outside of the shaded region is zero. For which of the loops is the magnitude of the induced current the greatest?

a) Loop 1
b) Loop 2
c) Loop 3
d) Loop 4

Answer 1

The magnitude of the induced current in a loop depends on the rate of change of magnetic flux. Loop 2 has the greatest rate of change of magnetic flux, resulting in the greatest induced current.

Step-by-step explanation:

The magnitude of the induced current in a loop is determined by the rate at which the magnetic flux through the loop changes. According to Faraday's law of electromagnetic induction, the greater the rate of change of magnetic flux, the greater the magnitude of the induced current. In this case, as the loops move upward through the uniform magnetic field, the area of the loops enclosed by the magnetic field is changing.

Loop 1 has a constant area enclosed by the magnetic field, so there is no change in magnetic flux and no induced current. Loop 2 is increasing the area enclosed by the magnetic field, resulting in a positive change in magnetic flux and an induced current. Loop 3 is decreasing the area enclosed by the magnetic field, resulting in a negative change in magnetic flux and an induced current. Loop 4 is also increasing the area enclosed by the magnetic field, but at a slower rate than Loop 2, resulting in a smaller induced current.

Therefore, the magnitude of the induced current is greatest in Loop 2.