Final answer:
To find the average emf induced in the coil, use Faraday's law of electromagnetic induction and calculate the change in magnetic flux. For the given values, average emf = (0.060 T - 0.050 T) * A * N / (0.10 s). The same formula can be used to find the induced emf for a decrease in magnetic field strength.
Step-by-step explanation:
(a) To find the average emf induced in the coil, we can use Faraday's law of electromagnetic induction which states that the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit. The magnetic flux through each loop of wire can be calculated by multiplying the magnetic field strength by the area of each loop, and since the magnetic field is perpendicular to the surface of each loop, the magnetic flux through the entire coil is simply the magnetic flux through each loop multiplied by the number of turns. Therefore, the average emf induced in the coil is given by:
emf = (change in magnetic flux) / (change in time)
In this case, the change in magnetic flux is equal to the change in the magnetic field strength multiplied by the area of each loop multiplied by the number of turns:
Change in magnetic flux = (B2 - B1) * A * N
Substituting the given values, we have:
emf = (0.060 T - 0.050 T) * A * N / (0.10 s)
(b) To find the value of the induced emf if the magnitude of the magnetic field decreases from 0.060 T to 0.050 T in 0.10 s, we can use the same formula as in part (a), but with the change in magnetic field being negative:
emf = (0.050 T - 0.060 T) * A * N / (0.10 s)
Where emf is the induced emf, B1 is the initial magnetic field strength, B2 is the final magnetic field strength, A is the area of each loop, N is the number of turns, and t is the time interval.
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