Answer :
133-turn coil and a changing magnetic field strength over a specific time interval, the magnitude of the average emf is determined to be 84.06 millivolts.
The average emf induced in a coil can be calculated using Faraday's law of electromagnetic induction, which states that the emf induced in a coil is equal to the rate of change of magnetic flux through the coil. The magnetic flux is given by the product of the magnetic field strength, the area of the coil, and the cosine of the angle between the magnetic field and the normal to the coil.
In this case, the coil has 133 turns and a radius of 2.55 cm, so its area can be calculated as A = π[tex]r^{2}[/tex] = π(2.55 cm[tex])^{2}[/tex]. The change in magnetic field strength is from 53.3 mT to 98.1 mT over a time interval of 0.197 s.
To calculate the average emf, we first need to calculate the average magnetic flux through the coil. The average magnetic field strength is the average of the initial and final values, (53.3 mT + 98.1 mT)/2 = 75.7 mT. The average magnetic flux is then given by Φ_avg = B_avg * A * cosθ, where θ is the angle between the magnetic field and the normal to the coil (which is 90 degrees since the field is perpendicular to the coil).
Finally, the average emf is calculated using the formula E_avg = ΔΦ_avg / Δt, where ΔΦ_avg is the change in average magnetic flux and Δt is the time interval. Substituting the values, we get E_avg = (Φ_final - Φ_initial) / Δt = (B_final * A * cosθ - B_initial * A * cosθ) / Δt.
Plugging in the given values, we find E_avg = (98.1 mT * π(2.55 cm[tex])^{2}[/tex] - 53.3 mT * π(2.55 cm[tex])^{2}[/tex]) / 0.197 s. Evaluating this expression yields E_avg = 84.06 mV. Therefore, the magnitude of the average emf induced in the coil during this time interval is 84.06 millivolts.
Learn more about Faraday's law here:
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