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Precise magnetic field inside solenoid
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ricko_uk:
Hi All,
I am trying to find an accurate formula for the magnetic field strength/density along the Z (revolution) axis of a solenoid. I need to input it in Excel so I can play with the values.
No idea how to use/calculate integrals in Excel so if possible either a formula that can be approximated to a non-integral reduction of it or if someone has one already in Excel and is willing to share it that would be great.
As input ideally the physical dimensions as well as the current. As output the strength along the Z axis of the solenoid.
ALSO A QUESTION: One thing I noticed is that a lot of the formulas I came across don't account for the length of the solenoid (just the number of turns). Am I right in thinking that 500 turns on a single layer product a different magnetic field density/strength inside the solenoid along its rotation axis which is different if it were 100 turns but on 5 layers (hence the length one fifth of the previously mentioned one)?
Thanks
Rick
Conrad Hoffman:
I'd just use FEMM, free to download.
T3sl4co1l:
The formulas you're seeing are for the infinite solenoid, which doesn't help much.
Try: https://paginas.fe.up.pt/~ee08173/wp-content/uploads/2014/03/finite-solenoid.pdf
Looks like the axial solution avoids scary integrals and simplifies to an Excel-able formula. Note, the brackets-sub/superscript notation I believe is saying you need to take the difference of the expression evaluated at the two values of ξ (and ξ is given elsewhere).
For a flat field over a region of space (i.e., dB/dx --> 0, and higher derivatives and other axes if possible), consider Helmholtz coils. There are at least two well-known cases (2 and 4 loops, giving 1st and 2nd derivatives, respectively). This will be much flatter than a solenoid.
You could also -- since this is a symbolic solution, take the derivative, and put two solenoids together such that their derivatives exactly cancel at the point of interest. Making a Helmholtz coil with finite length loops. May allow higher flux density for a given amount of wire and power dissipation?
I suppose ideally you'd want to integrate over a range of r as well, to get a range of radii, modeling a finite thickness solenoid -- a multilayer one, perhaps.
But yeah, things quickly get complicated in that direction, and you'll find it very attractive to get more tools, or simply model everything in the first place. You might pick up Maxima to automate symbolic math. You can perform a numerical integration in Excel by entering the formula across a large enough array of cells, and summing their results -- Riemann summation. Or, learn FEMM, as mentioned. ;D
Tim
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