# Electromagnet force and magnetic permeability

In a cylindrical core electromagnet,

Magneto-motive force (MMF) = 613 At

Magnetic strength (H) = 15345 At/m

I am using an iron core with 10% silicon in it, so the saturation magnetic flux density of that core is 1.95 T and absolute permeability (μ) = 1.2708·10-4 H/m. Area of cross-section (A) of the core = 1962.6 mm2.

I am having trouble calculating the force exerted by this electromagnet on a ferrous material at a distance (d) of 3 mm.

Substituting the above values in the formula, we get:

$$\F_1 = 0.5\cdot\mu\cdot A\cdot \left({MMF \over d}\right)^2 = 5222~\text N\$$

This force seems like too much.

Permeability of free space (μ0) = 1.2566·10-6 H/m.

If we use μ0 instead of μ, we get:

$$\F_2 = 0.5\cdot\mu_0\cdot A\cdot \left({MMF \over d}\right)^2 = 51~\text N\$$

Which one is correct and why? • The distance of 3mm is through air, so you need to use air permeability. Dec 25, 2021 at 15:20
• Thanks, Neil. So, the core does not affect the magnetic force outside the coil? Dec 25, 2021 at 15:42
• The core reduces the reluctance of the entire circuit, which increases the magnetic field you can sustain in the airgap. However when you do the virtual energy balance thing, effectively all the energy is stored in the airgap, and that's the thing that changes volume when you move a pole, so that's the permeability you have to use. Dec 25, 2021 at 16:14
• Thank you for your clarification, Neil. Dec 25, 2021 at 17:02
• I didn't ask you to reiterate what you'd already written, I asked you what numbers you mangled to get to H=15k At/m from MMF = 600 At. At a distance of 3 mm might mean an air-gap of 6 mm as you go out and return, or is the plate 1.5 mm away? This is why I asked for a diagram. Dec 25, 2021 at 19:02

Short Story: The core's permeability is only relevant when the gap is virtually zero.

Longer Story: The "resistance" of the core to produce a magnetic field from a given number of ampere turns (per metre) is called reluctance and, for iron/steel, that reluctance is quite low low but, only when used in a closed loop. When a gap is introduced, the reluctance of air becomes in series with the core and, that reluctance is massive compared to the reluctance of the iron/steel.

It's like having a 1 kΩ resistor (air) in series with a 10 Ω resistor (iron). The net resistance is still about 1 kΩ. And, it's the same for iron with even a quite moderate air gap.

But, it's not the gap between North iron pole face and ferrous target-piece that is significant here; it's the gap from the target-piece all the way back to the south pole face and that is pretty much constant and, excessive: - Short answer: Use $$\\mu_0\$$ and not $$\\mu_{IRON}\$$

• You're good with diagrams Andy, put one up to illustrate the configuation you're assuming. I'm sure from the numbers that there is some crossed assumption between the OP and us. Dec 26, 2021 at 6:52
• @Neil_UK done cause the OP provided his picture! Dec 26, 2021 at 9:56
• @Andy aka Thank you so much! Dec 26, 2021 at 11:14
• @RoshanZameer if we're done then please take the 2 minute tour to understand how to say thank you more appropriately!!! Dec 26, 2021 at 11:18