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I am sorry if this question is a bit silly, but I don't really know how to calculate the electromagnetic force between a magnet and an iron piece if they are not parallel to each other. The illustration is attached here. Any kind of help would be greatly appreciated. Thank you very much.

enter image description here

Kelvin Febianto Galiny
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    Do you know how to calculate it if they ARE parallel? – Andy aka Jun 16 '19 at 16:10
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    I believe this is the correct formula: F= A∙μ0. ((NI)^2)/2∙(g^2) , where μ0 is a constant, A is the area of the metal piece, N is number of turns of coil, I is current, and g is the gap length between the magnet and the metal piece. If it's parallel, then the value of 'g' can be determined and it's the same throughout the surface of the magnet. I hope I didn't make a mistake on this. – Kelvin Febianto Galiny Jun 16 '19 at 16:19
  • Split the problem into two scenarios; one at 5 mm and one at 2 mm and see how the answer is different to the case of assuming an average distance of 3.5 mm. If significant then break the problem down to 4 pieces. Rinse and repeat until you are happy with a reasonable answer. – Andy aka Jun 16 '19 at 16:25
  • Instead of trying to calculate it exactly (which, looking at your equation, you can't, since that's an approximation), calculate the worst case, which would be if the iron plate was flat at 5 mm. If whatever you're doing can work when it's at 5 mm, then it will work when it's at 2 mm. See it as a guarantee, if B is easier to pull than A, and you are strong enough to pull A, then you are also strong enough to pull B. And in the end, I think this is what you really care about right? Not the actual numbers. – Harry Svensson Jun 16 '19 at 16:52
  • Since the field lines get warped, will crude FEM even work? – analogsystemsrf Jun 16 '19 at 23:12
  • Yes, I've experimented this on my thesis project and it works, but it's better if I can at least do a mathematical calculation on it, since I need to include it in my thesis paper. – Kelvin Febianto Galiny Jun 17 '19 at 03:51
  • I think I'll include an approximation instead like you guys have told me. Thank you for the suggestion – Kelvin Febianto Galiny Jun 17 '19 at 04:03

2 Answers2

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This problem is pretty complex. There is no simple equation to solve a problem like this. It would involve a lot of 3d, surface,line integrals, and differential equations to solve it by hand. This would be graduate level mathematics, and not something you learn in undergraduate studies.

If you want an accurate approximation, I would suggest using an electromagnetic simulation software such as Ansys Electromagnetics.

Learning to use these softwares are much more practical and will help you in the long run. Hopefully this helps.

Dustin K
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  • I've thought about using integration in my calculation before but I never thought it would be so complex. Thank you very much for the information, the software will surely help me a lot. – Kelvin Febianto Galiny Jun 17 '19 at 03:56
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When it is coplanar with the surfaces greater than the concentration flux area, B field is linear and Force is inverse squared with gap, g.

  • when it is on edge, It is a line field with B field sensitivity 1/g and force is g^-4.

    • thus when tilted slightly, the force will be some inverse exponent greater than 2 but much less than 4.
    • when the surface area is not much greater than B field area, then there is leakage flux and exponent may be less than 2.

If you follow my logic, then you may compute more accurately, but it is more complex than this.

Tony Stewart EE75
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