Final answer:
To determine the magnitude of the average induced emf in the loop, use Faraday's law of electromagnetic induction. The induced emf is found by dividing the change in magnetic flux by the time interval, yielding an average induced emf of 0.40212 V.
Step-by-step explanation:
The question involves calculating the magnitude of the average induced electromotive force (emf) in a wire loop due to a changing magnetic field, which is a fundamental concept in physics, specifically in the area of electromagnetism. According to Faraday's law of electromagnetic induction, the induced emf in a loop is proportional to the rate of change of magnetic flux through the loop.
To find the induced emf, we use the equation:
emf = - Δ(B × A) / Δt
where:
- B is the magnetic field (T)
- A is the area of the loop (m²)
- Δt is the time over which the change occurs (s)
Given the data:
- Initial magnetic field B initial = 0.70 T
- Final magnetic field B final = -0.10 T (direction is reversed)
- Radius of the loop r = 0.40 m
- Time interval Δt = 1.0 s
We calculate the change in magnetic field ΔB:
ΔB = B final - B initial = -0.10 T - 0.70 T = -0.80 T
The change in flux Δ(B × A) is:
Δ(B × A) = ΔB × A = -0.80 T × (π × r²) = -0.80 T × (π × (0.40 m)²)
Calculating the area A of the loop:
A = π × r² = π × (0.40 m)² = 0.50265 m² (approximately)
So the change in flux is:
Δ(B × A) = -0.80 T × 0.50265 m² = -0.40212 T·m²
We can now find the induced emf:
emf = - Δ(B × A) / Δt = - (-0.40212 T·m²) / 1.0 s = 0.40212 V
Therefore, the magnitude of the average induced emf in the loop during this time is 0.40212 V.