A generator has a square coil consisting of 700 turns. The coil rotates at 78 rad/s in a 0.21-T magnetic field. The peak output of the generator is 120.00 V. What is the length of one side of the coil?
To find the length of one side of the coil, we need to use the formula for calculating the electromotive force (EMF) induced in the coil by a magnetic field:
EMF = N * B * A * ω,
where EMF is the electromotive force, N is the number of turns in the coil, B is the magnetic field strength, A is the area of the coil, and ω is the angular velocity.
In this case, we are given:
EMF = 120.00 V (peak output)
N = 700 turns
B = 0.21 T (magnetic field strength)
ω = 78 rad/s (angular velocity)
We can rearrange the formula to solve for the area of the coil (A):
A = EMF / (N * B * ω).
Now, let's substitute the given values and calculate the area:
A = 120.00 V / (700 turns * 0.21 T * 78 rad/s)
A = 0.00194444 m^2.
Since the coil is square, the area of the coil is equal to the length of one side squared:
A = x^2, where x is the length of one side of the coil.
x^2 = 0.00194444 m^2.
Taking the square root of both sides, we get:
x = √(0.00194444 m^2).
Calculating the square root:
x = 0.0441 m, or approximately 4.41 cm.
Therefore, the length of one side of the coil is approximately 4.41 cm.