Final answer:
Using Faraday's law, one can calculate the induced emf in the coil as it's equal to the rate of change of magnetic flux. The magnetic flux is found by multiplying the magnetic field, area of the coil, number of turns in the coil and cos(θ). The difference in the magnetic flux at times t2 and t1 divided by the time difference will give the induced emf.
Step-by-step explanation:
The electromagnetic induction problem can be solved with Faraday's law which states that induced emf in the coil equals the rate of change of magnetic flux. In this case, the magnetic flux equals to the product of magnetic field B, area of the coil A, number of turns in the coil N and cos(θ) where θ is the angle between magnetic field and normal to the coil. Here, θ = 60°, A = 0.187 m², N = 251, and B is varying with time that is given by B=0.013t³+0.17t²+0.221t. To find the induced emf, you need to calculate the difference of the magnetic flux at times t=4.22 s and t = 1.76 s.
To find the induced emf in the coil between time intervals t1 = 1.76 s and t2 = 4.22 s, we need to calculate the change in magnetic flux through the coil during this time period. The magnetic flux is given by the product of the magnetic field and the area of the coil. We can then use Faraday's law to calculate the induced emf. The formula for emf can be written as ε = -dΦ/dt, where ε is the induced emf, Φ is the magnetic flux, and t is the time. Firstly, calculate magnetic flux at t=1.76 s and t=4.22 s. After that, subtract the value of flux at t=1.76 s from the flux at t=4.22 s. The absolute value of the result gives the change in magnetic flux. Secondly, the rate of change of magnetic flux is obtained by dividing the change in flux by the time difference (t2 - t1). Finally, the induced emf equals to the rate of change of magnetic flux, according to Faraday's law.
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