Final answer:
To calculate the change in magnetic flux and the induced emf in the coil, Faraday's Law is applied, taking into account the magnetic field strength, the number of turns in the coil, and the area and time over which the change occurs.
Step-by-step explanation:
The scenario described in the question relates to Faraday's Law of electromagnetic induction, which explains how a change in magnetic flux through a coil generates an induced electromotive force (emf). The change in magnetic flux (ΔΦ) is calculated using the formula ΔΦ = B × A × N, where B is the magnetic field strength, A is the area of the coil, and N is the number of turns in the coil. Given a uniform magnetic field with a strength of 1.50 T, a coil with 50 turns, and the area of the coil changing from 0.250 m² to 0 m², the change in magnetic flux comes out to ΔΦ = 1.50 T × 0.250 m² × 50 turns. Since the area goes to zero, the total change in flux is 1.50 T × 0.250 m² × 50. To calculate the induced emf (ε), the formula ε = -N × (ΔΦ/Δt) is used, where Δt is the time in which the change occurs. By substituting the given values, one can calculate the induced emf and its direction according to Lenz's Law.