Final answer:
The final value of the loop's area after 2.72 seconds is 1.0991 m², calculated by using Faraday’s Law of Induction and given the constant magnetic field of 0.890 T, an initial area of 0.610 m², and an induced voltage of 0.160 V over that period.
Step-by-step explanation:
The student is dealing with the concept of electromagnetic induction, specifically Faraday's Law of Induction, which states that the induced electromotive force (EMF) in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit. In this case, the magnetic field is constant and the change in flux is due to the change in area of the wire loop.
In order to find the final value of the loop's area, we can use Faraday’s Law in the form of E = - (change in flux)/(change in time). Since the initial magnetic flux is the initial area multiplied by the constant magnetic field, and the final flux is the final area times the constant magnetic field, we can substitute and solve for the final area.
Given that the induced voltage (E) is 0.160 V, time (t) is 2.72 s, and initial area (Ai) is 0.610 m², we have:
Change in flux = E * t = 0.160 V * 2.72 s = 0.4352 Wb (since 1 V * s = 1 Wb).
Since flux = magnetic field (B) * area (A) and the initial flux is B * Ai, the change in flux is B * (A f - Ai), where A f is the final area. Therefore, dividing change in flux by the magnetic field B gives us the change in area, which can then be used to find A f. With the magnetic field B being 0.890 T:
Change in area = 0.4352 Wb / 0.890 T = 0.4891 m²
A f = Ai + Change in area = 0.610 m² + 0.4891 m² = 1.0991 m².
Therefore, the final value of the loop's area after 2.72 seconds is 1.0991 m².