I am doing some research involving solenoids of varying aspect ratios, and I'm looking for some equations I can use to back it up. I have three different solenoids of the equal n (where n=N/L), with different shapes and different cores/plungers, and I am comparing their forces by testing them with the same current through the wire. Ideally the aspect ratio of the plungers would be my only variable, but there are other variables that I would like to compensate for by using equations.(adsbygoogle = window.adsbygoogle || []).push({});

First, as I understand it, the flux density in a round solenoid is basically

B = μnI.

One of my solenoids (square plunger) is about 9300 turns/m with plunger area 1E-4 m[itex]^{2}[/itex] running 1.5A. I'm using a mild steel core with a rough estimate of μ[itex]_{r}[/itex]=50. By the above equation, the field from my solenoids is predicted about 0.88 T. Does that sound logical?

Also I have found a force equation that I don't know whether to believe:

F = B[itex]^{2}[/itex]A/(2μ[itex]_{0}[/itex])

(the force exerted on the solenoid plunger). Does anyone have a correction for this? This equation is predicting ~28 N and I'm getting ~0.35 N from that particular solenoid. Having an accurate force equation would be a huge help.

I tested my solenoids on an Instron tester machine. The peak forces for the highest-aspect-ratio solenoid were highest, followed by my medium-aspect-ratio solenoid, and then the one with the square plunger was the least. I'm pretty sure this is because the higher-aspect-ratio solenoids have a larger length of wire per coil. So I think the field for these rectangular-core solenoids might be:

B = μnI + (2)μ[itex]_{0}[/itex]I/(2πr)

where the latter term is the field about a straight length of wire, and each wrap of the coil has two lengths (one above and one below the plunger).

Then, for the force of the rectangular-core solenoids, I would add the term NILB to the regular force equation. Does that seem right?

Thanks for the help; sorry for the long post.

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# Peak forces of round and rectangular solenoids

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