$$F = (N⋅I)^2⋅uA/(2g^2)$$

  • F = Force
  • I = Current
  • N = Number of turns
  • g = Length of the gap between the solenoid and the magnetizable metal
  • A = Area

Does it assume a solenoid of zero length and does it also make assumptions about the magnetic susceptibility or permeability of the metal it is attracting? And is g the gap between the metal and centre of the solenoid or the end.


1 Answer 1


The assumptions are a metal of infinite permeability. Seeing as most magnetic metals have ur > 1000, that's pretty good.

Having made that assumption, there's no need to define anything about the geometry of the solenoid, it's all down to the gap and the area of the gap, as long as the gap is fairly small.

  • \$\begingroup\$ 1. What is the area of the gap? 2. gap between each turn of the solenoid is a different distance (the wire stack on top of each other) does that mean we need to integrate in relation to distance? 3. isn't magnetic susceptibility the deciding factor on how the metal is influence not permeability? \$\endgroup\$
    – Leo
    Mar 10, 2020 at 12:15
  • \$\begingroup\$ 1) The air gap has a volume. You know the length of the gap. The area of the gap is its volume/area. 2) Doesn't matter as long as the airgap length is small enough, and the material permeability high enough. 3) neglecting geometrical constants, they are the same thing. Permeability is a material property independent of geometry, so we tend to talk in that. It's the susceptibility of the airgap that matters, the susceptibility of the metal path will be a lot smaller, for a properly designed magnetic attraction solenoid. \$\endgroup\$
    – Neil_UK
    Mar 10, 2020 at 13:44
  • \$\begingroup\$ Don't we also assume that the magnetizable metal at the end of the solenoid is infinitely large? If you put a 0.001 g piece of magnetizable metal at the end of the solenoid is that different than a 10kg piece? What if there is no magnetizable metal at the end of the solenoid, wouldn't the force go to zero? There have to be a ton of assumptions related to that magetizable metal. \$\endgroup\$
    – Luminaire
    Aug 13, 2020 at 20:32

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