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i am developing a home-made generator but i am having some trouble with coil design.

Going on Faraday's induction formula :

V = N A (2 pi RPM/60) B

a 50 turn coil with a radius of 20mm going at 20,000 RPM should give me 80 volts or so, in practice i am getting much less than this.

Does wire gauge have no bearing on induction, i would have thought that a finer wire would give me a higher voltage ?

Any help greatly appreciated,

DC.