Final answer:
The problem can be solved using Faraday's law of electromagnetic induction and Lenz's law, which state that the induced EMF in a circuit is proportional to the rate of change of the magnetic flux and is in the direction to oppose the change that caused it.
Step-by-step explanation:
This physics question involves concepts related to electromagnetism, particularly the Faraday's Law of electromagnetic induction. This law states that the electromotive force (EMF) induced in a circuit is equal to the time rate of change of the magnetic flux through the circuit.
Given the circular wire loop has a diameter of 41cm (which gives a radius, r, of 20.5 cm or 0.205m), with its resistance being 120 Ohms, and the magnetic field, B, increases from 5mT to 55mT in 25ms, we can apply Faraday's law to calculate the change in the magnetic field which is ΔB = B_final - B_initial = 55mT - 5mT = 50 mT or 0.05 T.
The change in magnetic flux, ΔΦ, is equal to the change in the magnetic field, ΔΦ = ΔB * Area = ΔB * πr^2. Hence, the induced electromotive force (EMF) or voltage across the wire is equal to the rate of change of the magnetic flux according to Faraday's law, which is -dΦ/dt = EMF. The negative sign indicates that the induced EMF and the change in magnetic flux have opposite directions, according to Lenz's law.
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