Final answer:
The maximum induced emf in a rectangular loop spinning in a magnetic field is achieved when the change in magnetic flux is maximum, which occurs due to Faraday's law of electromagnetic induction.
Step-by-step explanation:
The induced emf in a rectangular loop of wire that is placed perpendicular to a uniform magnetic field and then spun around one of its sides will be maximum when the change in magnetic flux is at a maximum. This situation occurs because of Faraday's law of electromagnetic induction, which states that an induced emf is proportional to the rate of change of magnetic flux through a circuit.
Magnetic flux (Φ) is given by Φ = B × A × cos(0), where B is the magnetic field strength, A is the area of the loop, and 0 is the angle between the magnetic field and the normal to the surface of the loop. The flux is maximum when the field is perpendicular to the loop (θ = 0 degrees) and minimum when the field is parallel to the loop (θ = 90 degrees). However, the maximum emf is induced not when the flux is at maximum or minimum, but when the change in the flux is greatest, which is when the loop is at positions where it is sweeping through the magnetic field lines at the fastest rate (i.e., passing through θ = 90 degrees during its rotation).