Final answer:
The magnitude of the induced current in the coil is 0.5 A, calculated using Faraday's law and Ohm's law, given the changes in the magnetic field, coil area, number of turns, time interval, and resistance.
Step-by-step explanation:
The student's question relates to Faraday's law of electromagnetic induction and Ohm's law in the context of a changing magnetic field inducing an emf (electromotive force) and subsequently a current in a coil. To find the magnitude of the induced current in the coil, we need to calculate the change in magnetic flux and use Ohm's law.
Firstly, we find the change in magnetic flux (ΔΦ), which is given by the formula: ΔΦ = ΔB × A × N, where ΔB is the change in magnetic field, A is the area of the coil, and N is the number of turns.
The induced emf (ε) is given by Faraday's law: ε = - ΔΦ / Δt, where Δt is the time over which the change occurs. Since ε = I × R (where I is current and R is resistance), we can rearrange to find I: I = ε / R.
Using the given values: ΔB = 6 T - 2 T = 4 T, A = 50 cm² = 0.005 m², N = 20 turns, Δt = 2 s, and R = 0.4 Ω, we will calculate ε and then I.
ΔΦ = 4 T × 0.005 m² × 20 = 0.4 Wb (Weber),
ε = - 0.4 Wb / 2 s = - 0.2 V (ignoring the negative sign as we're asked for magnitude),
I = 0.2 V / 0.4 Ω = 0.5 A.
Therefore, the magnitude of the induced current in the coil is 0.5 A.