Final answer:
The magnitude of the average emf Eₐᵥ induced in the coil during the interval is 6.62 millivolts.
Step-by-step explanation:
When a coil is subjected to a changing magnetic field, an electromotive force (emf) is induced within it, following Faraday's law of electromagnetic induction. The formula to compute the induced emf in a coil is given by ε = -NΔΦ/Δt, where ε represents the induced emf, N is the number of turns in the coil, ΔΦ denotes the change in magnetic flux, and Δt is the time interval.
Given that the coil has 103 turns and a radius of 2.05 cm, first, we need to determine the change in magnetic flux (∆Φ). As the magnetic field strength changes from 54.7 mT to 94.1 mT over a time interval of 0.185 s, the change in magnetic field (∆B) can be calculated as 94.1 mT - 54.7 mT = 39.4 mT.
The formula for the magnetic flux through a coil is Φ = BA, where B is the magnetic field strength and A is the area of the coil. As the coil is a circular one, the area A = πr^2, where r is the radius. Hence, the initial magnetic flux Φ₁ = π(2.05 cm)^2 * 54.7 mT and the final magnetic flux Φ₂ = π(2.05 cm)^2 * 94.1 mT.
Subtracting Φ₁ from Φ₂ gives us the change in magnetic flux (∆Φ). Finally, using the formula ε = -NΔΦ/Δt, where N = 103 turns and Δt = 0.185 s, we calculate the induced average emf Eₐᵥ. Upon computation, the average emf Eₐᵥ is found to be 6.62 millivolts.