# Solenoid Optimization

Alex Sieber
First time posting here so excuse me if I don't know the rules so well. I figured this would be the best place to post this question.

I'm trying to optimize the force produced by a solenoid that is no bigger than 15mm in diameter (D). My goal is to get just the right balance of number of wire wraps (N), gauge of wire (G) and radius of the area inside the solenoid (R). I found an equation online that expresses the force of a solenoid on a piece of metal here:

http://www.daycounter.com/Calculators/Magnets/Solenoid-Force-Calculator.phtml

however I believe this is just an approximation under extreme circumstances. Using the variables previously expressed I have that D = R + Nd, where d is the diameter of the gauge of wire I'm to use. I know that the force is proportional to the number of wraps (N) and the current (i), however I also am under the impression that the resistance, and therefore the current, depends on the length and area of the wire. Does anyone know the proper ratio of open radius (R), to number of wraps (N), to gauge of wire (G) that would produce the largest force? I have a bunch of derivations using the equation from the aforementioned link and would be happy to provide my conclusions, however I would like to receive your guys' input before laying it all out. Thank you for any assistance you can provide and I'm happy to become to a part of the community here!

If my point isn't clear here's an example:

Solenoid 1: Has open radius of R=3.6mm inside the solenoid, a wire gauge of G=16 and N=3 wraps per unit length.
Solenoid 2: Has open radius of R=5mm inside the solenoid, a wire gauge of G=19 and N=3 wraps per unit length.

Does solenoid 1 or 2 exert a larger force on a piece of metal, say, 20mm, away from the end of the solenoid?

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