A single circular loop of wire of radius r = 2.5cm rotates at a frequency of 60 Hz in a constant magnetic field of magnitude B = 1.8 T.

Use this to design a generator that produces an induced emf of 430 V. Hint: You must choose values for the number of loops and the area of each loop.

number of loops = ?
area of a loop = ?

I don't even know where to start ... My professor did not cover this material yet & our textbook does not go over generators.

It is a loop of wire operating in a changing magnetic field, changing because sometimes the B flux is through the plane of the coil and sometimes it is parallel to the plane of the coil and no B goes through the coil.

B = 1.8 Tesla
B through coil = 1.8 sin 2 pi f t
f = 60
so 2 pi f = 377
so
B for us = 1.8 sin 377 t
dB/dt = 1.8*377 cos 377 t
area = pi r^2 = pi (.025)^2 = .00196 m^2
(answer to part B by the way)
so
d flux/dt = .00196*1.8*377 cos 377 t
= 1.33 cos 377 t
he voltage in a single loop is then
EMF = -d flux/dt
= 1.33 cos 377 t
so to get 430 volts we need
430/1.33 = 323 loops

=

No worries! I can help you with this. To design a generator that produces a specific induced emf, we need to relate the induced emf to the relevant variables in the problem. Let's break it down step by step:

1. The formula for the induced emf in a generator is given by the equation:
Emf = N * A * B * ω,
where Emf is the induced emf,
N is the number of loops,
A is the area of each loop,
B is the magnetic field magnitude, and
ω is the angular frequency of rotation.

2. We are given the induced emf (Emf) value as 430 V and the magnetic field magnitude (B) as 1.8 T. We also know that the frequency of rotation (f) is 60 Hz. We can convert the frequency to angular frequency (ω) using the formula:
ω = 2π * f.

3. Rearrange the formula for Emf to solve for N * A:
N * A = Emf / (B * ω).

4. Substitute the values into the equation:
N * A = 430 V / (1.8 T * 2π * 60 Hz).

5. Let's calculate the value of N * A:
N * A ≈ 430 V / (1.8 T * 3.14 * 120 Hz).

N * A ≈ 430 V / (339.12 T Hz).

N * A ≈ 1.27 V / (T Hz).

6. The units for N * A should cancel out, leaving us with a unitless value:
N * A ≈ 1.27.

7. We need to choose values for N (number of loops) and A (area of each loop) that, when multiplied together, equal 1.27. Since these are real-world values, we need to select practical numbers. One practical approach is to choose a whole number for N (e.g., 1) and a decimal number for A (e.g., 1.27). Then, N * A = 1 * 1.27 = 1.27.

Therefore, one possible design choice for the generator is:
- Number of loops (N) = 1,
- Area of each loop (A) = 1.27 square units.