# Faradays Law, The correct version

1. Jan 22, 2010

### keith03

I see this formula destroyed all over the net. I am building a generator, and I have found that some error has been made in the manipulation of Faradays Law. If my derivation is correct, then I need somebody to tell me how to more accurately calculate the area of my coils. (This is the only variable I can think of that I will keep this from working) I have made a prototype, and my expected results should be slightly lower than my calculations due to losses. Here is the manipulation I have made. This is in refrence to an axial flux design. A rotor of magnets in alternating pole configuration is spun past a stator of coils. The rotor has 12 magnets total. I am saying this because it effects the rate of change of flux for one revolution. The magnets are circular, and the coils are in the shape of a trapezoid.

EMF= N* (Rate of change of flux/rate of change in time)

I justified the following per my own derivation.

N = Number of turns per coil
P = number of poles. (2 poles make one cycle of AC EMF)
A = EFFECTIVE area of the coil in [square meters]
Bm = flux density at the coil [Teslas]
n = revolutions per second

The flux changes 12 times for every revolution.
the frequency of the flux change is 2*PI*f = 2*PI*((P/2)*n)

Since this incorporates the rate of change in time...

(P/2) is one complete AC cycle on a coil

EMF = 2*PI*((P/2)*n)*A*Bm

I have made a prototype of the generator and the EMF produced is way higher than the calculated values. The closest equation that matches the resulted output is:

EMF = Bm*l*v (multiplying this by N)

l= 2*PI*r (of the single strand of wire)

I multiply this by the number of turns, and the answer is slightly higher than the result.

Please verify my work. I am ready to spend a lot of money to complete this, and I would like to have my calculations match, or come close to by logical analysis, of my results.