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I'm trying to make an electro-magnet and I want to figure out what core and wire I need using math instead of trial-and-error.

I want it to produce ~1.5 newtons of force at ~1.5 inches from the magnet. The best equation I found for it was on this website, which is: $$ F = n I^2 \mu_0\frac{A}{2d^2} $$ where:

  • \$F\$ is the force in newtons
  • \$n\$ is the number of turns
  • \$I\$ is the current
  • \$μ_0\$ is the permeability of free space
  • \$A\$ is the cross-sectional area of the solenoid
  • \$d\$ is the distance to the object to pull

What I'm worried about is that this equation doesn't consider the relative permeability of the core, the permeability of the object being lifted, or the magnetic saturation limit of the core. I couldn't find any better equations though.

Does anyone know of an equation that includes all the factors already there plus the ones I mentioned?

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  • \$\begingroup\$ Whether you need a specific formula depends on the diameter of the coil and core. The formula presented is probably for a homogeneous induction, which assumption only approximately holds if the diameter is much larger than the distance of 1.5 inch, which I find hard to believe. Therefore it would be in order to calculate the field's energy depending on the position of the core. Differentiating that with respect to the direction in which the core moves will yield the work, aka the force. \$\endgroup\$
    – HarryH
    Commented Mar 8 at 10:13
  • \$\begingroup\$ Can you give us a rough sketch of the configuration you have in mind? \$\endgroup\$
    – HarryH
    Commented Mar 8 at 10:16
  • \$\begingroup\$ Anyway, it you only need a usable formula in order to prevent going through a process of trial and error you could use the formula you presented and build in a inaccuracy factor of 2. The worst that can happen is that the electromagnet will be 2 times stronger than intended which you can overcome by lowering the current. Just be sure that 'your' formula fits the configuration you choose. \$\endgroup\$
    – HarryH
    Commented Mar 8 at 10:36

1 Answer 1

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What I'm worried about is that this equation doesn't consider the relative permeability of the core, the permeability of the object being lifted, or the magnetic saturation limit of the core. I couldn't find any better equations though.

Until the object to be attracted actually moves and touches the poles of the electromagnet, the massively biggest factor is the air-gap therefore' the relative permeability of the core and, the permeability of the object being lifted are irrelevant.

You might slightly need to be aware of the core saturation limits but in the main, the air-gap is the massive factor that largely prevents core saturation.

Does anyone know of an equation that includes all the factors already there plus the ones I mentioned?

There is no need for one.

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