Final answer:
To calculate the peak voltage of the described generator, Faraday's law is applied with the conversion of rpm to radians per second and area calculation from the coil diameter, resulting in a calculation involving the number of turns, area of the coil, magnetic field strength, and angular velocity.
Step-by-step explanation:
To calculate the peak voltage of a generator that rotates a 199-turn, 0.100 m diameter coil at 3,500 rpm in a 0.700 T magnetic field, we can use Faraday's law of electromagnetic induction, which states that the induced emf (electromagnetic force, also known as voltage) in a coil is proportional to the rate of change of the magnetic flux through the coil. The peak emf (E) can be calculated using the formula:
E = NABωsin(ωt)
Where:
N is the number of turns in the coil
A is the area of the coil (in square meters)
B is the magnetic field strength (in teslas)
ω is the angular velocity of the coil (in radians per second)
ωt is the angle between the magnetic field and the normal to the coil
Since the coil rotates uniformly, the angle ωt changes with time and the sine function oscillates between -1 and 1, hence the term 'peak' voltage which corresponds to sin(ωt) being 1.
First, let's convert rpm to radians per second for the angular velocity:
ω = 3500 rpm × π/30 rad/min
Now, we can calculate the area (A) of the coil using the diameter:
A = π × (radius)^2 = π × (0.100 m / 2)^2
Finally, we can plug these values into the formula to find the peak voltage:
E = 199 turns × (π × (0.100 m / 2)^2) × 0.700 T × 3500 rpm × π/30 rad/min
When the calculation is carried out, we arrive at the peak voltage for the given generator.