Final answer:
Using Faraday's law of electromagnetic induction, the maximum induced EMF for a coil with 14 turns, a 0.10 m radius, a 1.6 T magnetic field, and a rotation frequency of 1.5 Hz is calculated to be 6.65 Volts.
Step-by-step explanation:
Calculating Maximum Induced EMF
To determine the maximum value of the induced electromotive force (EMF) in a coil rotating in a uniform magnetic field, we can use Faraday's law of electromagnetic induction. The formula for the peak induced EMF (ε_max) is given by ε_max = NABω, where N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity.
In this scenario, the coil with 14 turns (N = 14) with a radius of 0.10 m (A = π * (0.10 m)^2), a uniform magnetic field (B = 1.6 T), and a rotation frequency of 1.5 Hz is considered. First, we must convert the frequency to angular velocity (ω), which is done by ω = 2πf = 2π * 1.5 Hz. Then the equation can be used to find ε_max.
Let's calculate ω:
ω = 2π * 1.5 Hz = 9.42 rad/s
Now, we can compute the area (A):
A = π * (0.10 m)^2 = 0.0314 m²
Finally, we'll use the formula to find ε_max:
ε_max = NABω
ε_max = 14 * 0.0314 m² * 1.6 T * 9.42 rad/s = 6.65 V
Therefore, the maximum value of the induced EMF in the coil is 6.65 Volts.