Final answer:
Using Faraday's law of induction and Ohm's Law, we calculated the induced emf due to the change in the magnetic field, and then determined the magnitude of the induced current in a 125-turn circular coil, with the final answer being 0.80 A.
Step-by-step explanation:
To find the magnitude of the induced current in the coil, we first need to calculate the emf induced in the coil. We can use Faraday's law of induction, which states that the emf induced in a coil is equal to the negative change in magnetic flux (∆Φ) over the change in time (∆t), multiplied by the number of turns in the coil (N):
emf = -N ∆Φ / ∆t
The magnetic flux Φ is given by the product of the magnetic field (B) and the cross-sectional area (A) of the coil. In this case, we are given the change in the magnetic field along the axis of the coil. The cross-sectional area of the coil (A) is = π r^2, where r is the radius of the coil. Given a 125-turn circular coil with radius 48.0 cm and the change in magnetic field is from 2.40 T to 0.600 T over 1.90 seconds, we find:
A = π (0.48 m)^2
∆B = B_final - B_initial = 0.600 T - 2.40 T = -1.80 T
∆Φ = A ∆B = π (0.48)^2 × -1.80
∆t = 1.90 s
Then, we substitute A, ∆B, and ∆t into the equation for emf to get:
emf = -N ∆Φ / ∆t = -(125) ∆Φ / 1.90
To find the current (I), we use Ohm's Law, where I = emf/R, with R as the coil's resistance. Given the resistance R = 6.00 Ω
I = emf / R
Finally, we calculate the current and obtain the magnitude. The correct answer is option B) 0.80 A.