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I am building a simple electromagnet, with an Iron core, and want to calculate the force it can exert on another piece of Iron when in direct contact with it (Basically how much weight it can lift). Here are the parameters of my electromagnet:

Coil Turns = $200$
Length = $0.01$ (m)
Cross-sectional Area = $0.000314$ ($m^2$, $r = 0.01$ m)
Current = $1.79$ (amps, $V = 12, R = 6.7$)
Core's magnetic permeability = $6.3 * 10^{-3}$ (Iron)

I have a cylindrical iron core with a radius of 1 and height of 1 (cm) and am wrapping 200 turns of 0.2 mm thick copper wire around it. I plan on lifting a block of Iron with it, that is the maximum weight possible. The design is supposed to look like a miniature lifting electromagnet crane, similar to this:

The red lines show the coil wiring layout.

How can I calculate the force between the electromagnet and the block of iron?

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  • $\begingroup$ The units for length should almost certainly be meters, not millimeters. $\endgroup$
    – Michael Seifert
    Commented Jun 4, 2023 at 13:23
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    $\begingroup$ Something seems off about that formula, it calculates the force on what object? And, at what distance is said object? Usually forces of field like that fall inversely as some function of the distance $\endgroup$
    – Amit
    Commented Jun 4, 2023 at 13:58
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    $\begingroup$ @MahanLamee You could probably get an answer to your question if you phrase it more as "how do you calculate the force between an electromagnet and a piece of iron." It's not a simple answer and not generally covered in undergrad E+M. As others have noted, it doesn't look like you're using formulas that apply to your situation at all. I don't think this is a homework question at all... but the title sounds like the title of an undergraduate electrodynamics homework question. Then people click on the link and see simple E+M equations, so they vote to close without reading the question. $\endgroup$
    – AXensen
    Commented Jun 4, 2023 at 15:02
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    $\begingroup$ @MahanLamee It would be likely to be reopened if you removed the equations for $F$ and instead spent more time describing the geometry of your electromagnet and the geometry of the thing it's picking up. The second equation you have now has a symbol $g$ which is totally undefined... so that alone might get you closed for "not enough details or clarity." Especially if you made a simple drawing in microsoft paint or something. I for one will vote to reopen now. $\endgroup$
    – AXensen
    Commented Jun 4, 2023 at 15:16
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    $\begingroup$ @Mahan Lamee. Yes, with your figures I, too, get a huge force. I think that 5000 may be too large for $\mu_r$, but, as I've said, it's very difficult to find values for it. A centimetre is much too small, surely, for the length of the magnetic circuit, but multiplying it by 10 will only bring the force down by a factor of 100. Time for some experimental work, I think! $\endgroup$
    – Philip Wood
    Commented Jun 4, 2023 at 16:40

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