Final answer:
The maximum induced emf in a rotating circular ring subjected to a uniform magnetic field can be calculated using Faraday's law of electromagnetic induction and the geometric properties of the circular ring. Factors such as the area of the loop, the angular velocity, the number of turns in the loop, and magnitude of the magnetic field play significant roles in determining the induced EMF.
Step-by-step explanation:
The question is asking for the maximum induced emf in a rotating circular ring subjected to a uniform magnetic field. To find the induced emf in the ring, we can use Faraday's law of electromagnetic induction which states that the emf induced in a loop is equal to the rate of change of magnetic flux through the loop.
The formula that represents Faraday's law is as follows:
ε = -N ΔΦ/ Δt
Where:
- ε is the induced emf
- N is the number of turns in the loop
- ΔΦ is the change in magnetic flux
- and Δt is the change in time.
However, we must modify this equation a bit to fit our situation since we are dealing with a rotating ring in a uniform magnetic field. The magnetic flux Φ through the ring is given by Φ = BA cos(ωt), so its rate of change with respect to time t yields the maximum value when differentiated to give -BAω sin(ωt). The maximum value of sin(ωt) is 1, so the maximum induced emf ε_max is given by ε_max = N|ΔΦ/ Δt| = NBAω, where B is the magnetic field, A is the area of the loop, N is the number of turns, and ω is the angular velocity.
In this scenario, we can calculate:
- The area of the loop A using the formula for the area of a circle, A = πr^2, where r is the radius. Since we are given the diameter, the radius r is half the diameter, i.e., r = 0.1 m
- The angular velocity ω using the relationship between frequency f and angular velocity, ω = 2πf. The frequency f is given as 60 Hz Substitute the known values into the formula to find the maximum induced emf.
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