To find the total length of wire, Faraday's Law is applied using the provided values for induced emf, magnetic field change, and the number of turns. The area of the square-shaped coil is computed, enabling the determination of the side length and consequently, the total length of wire by accounting for all four sides and the number of turns.
The student's question involves a magnetic field and electrical induction, which are related to Faraday's Law of electromagnetic induction. According to Faraday's Law, 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. The formula to calculate the induced emf in the coil is given by ε = -N(dΦ/dt), where ε is the emf, N is the number of turns, and dΦ/dt represents the rate of change of magnetic flux. The flux change, Φ, is calculated by B*A*cos(θ), where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field vector and the normal to the coil's plane.
Since we are given the induced emf (ε = 80.0 mV), the number of turns (N = 50), the initial and final magnetic field (B - B = 600 μt - 200 μt), and the time interval (Δt = 0.400 s), we can use these to calculate the area, A, of the coil. Once the area is found, using the fact that the coil is square-shaped, we can calculate the side length and, from there, the total length of wire by multiplying the side length by 4 (since a square has four sides) and again by the number of turns (50).
To find A, we rearrange the emf equation to solve for A and then proceed with finding the side length and total length of wire. The total length will then be L = 4 * side length * number of turns.