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Faraday's law for a coil is :

V = A * M * N

Where: V = Peak output-voltage A = Area of the cross-section of the wire M = Rate of change of magnetic flux in the coil N = Number of turns of the coil

Question:

Whats happens when A gets very small and N very large? I expect that in that case internal resistance gets higher and the output voltage drops??

If that's true, there will be a certain combination of A and N that will be optimal for a needed V. Question: How to obtain this A and N ?

NB: By optimal I mean minimal space needed by the coil and minimal material costs for the wire.

edit: The coil is used as a generator like in a bike dynamo. So the coil is wound around a linear weak-iron core.

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    \$\begingroup\$ Every single part of your question, including the parts you didn't ask, have the answer "it depends". And that law, while it may be true for specific cases, doesn't cover the realities of solenoidal coils or coils wound on cores. Please tell us what specifically you're trying to do, e.g. build a radio, build a switching power supply, tug Mars out of orbit, achieve world domination, etc. \$\endgroup\$ – TimWescott Oct 16 '18 at 19:46
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I'm sure there's a professional tool, but I would just use a spreadsheet.

Choose your constants - wire diameter, hole diameter, length, etc, and let it work out Area and Nturns (assuming some wire filling fraction, maybe 50%), then V. , Also length of wire, and then resistance, and cost. Then play with the constants, try a few scenarios, even plot some graphs.

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  • \$\begingroup\$ Tom, can you please point me to a tool? \$\endgroup\$ – joop s Oct 16 '18 at 23:38
  • \$\begingroup\$ Excel :P But seriously, no professional tool will help you until you have the understanding you need to do it yourself. The hard part is expressing your desire in engineering terms. Solving it is easy after that. Read Wikipedia, look for online calculators, and then ask more questions here. \$\endgroup\$ – tomnexus Oct 17 '18 at 12:06
  • \$\begingroup\$ Besides Faraday's law, what formula's are relevant? Can't find any other on Wikipedia \$\endgroup\$ – joop s Oct 17 '18 at 16:58

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