Final answer:
The induced emf when a 50-turn coil in a 1.50 T magnetic field is stretched to no area in 0.100 s is counterclockwise with a magnitude of 7.5 V. This result is obtained by applying Faraday's Law of electromagnetic induction and considering Lenz's Law for the direction. Therefore, the correct answer to the question is option (D) Counterclockwise, 7.5 V.
Step-by-step explanation:
The question is asking for the direction and magnitude of the induced electromotive force (emf) in a coil when it is altered within a magnetic field, according to Faraday's Law of electromagnetic induction. In this scenario, a coil with 50 turns and an initial area of 0.250 m² is stretched to an area of zero in a uniform magnetic field of 1.50 T over a time of 0.100 s.
Using the formula for induced emf (ε = -N ( ΔΦ / Δt )), where N is the number of turns, Φ is the magnetic flux, and t is time, we can calculate the magnitude of the emf. The change in flux (ΔΦ) is BΔA, where B is the magnetic field strength and ΔA is the change in area. Given B = 1.50 T and ΔA = 0.250 m², N = 50 turns, and Δt = 0.100 s, the magnitude of the induced emf is 7.5 V.
The direction of the induced emf follows Lenz's Law, which states the induced emf will generate a current that opposes the change in magnetic flux through the coil. As the coil's area decreases, the number of magnetic field lines passing through it decreases, so the induced current will circulate in such a way as to try to maintain the magnetic field through the coil. Since the magnetic field is directed into the page, the induced current must be counterclockwise to oppose the reduction of the magnetic field lines, hence the induced emf is counterclockwise. Therefore, the correct answer to the question is option (D) Counterclockwise, 7.5 V.