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What's the theoretical potential for how strong electromagnets can get? If you just kept coiling a solenoid longer and wider, and fed more and more current into the coil, would the field strength in the middle get arbitrarily dense?

This is the closest related question I could find: How to wire a STRONG electromagnet?

I understand that the core will eventually saturate and thus stop helping to increase the field. But I think increasing the other parameters still makes for a stronger magnet.

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Superconducting magnets can get quite high fields, higher than the limit given by the core electromagnets, as the LHC experiments have demonstrated, but are subject to limitations of the cryogenics and the materials:

Superconducting magnets must operate below both the critical temperature and the critical field of the material from which they are constructed.

Careful design is used to find a fine balance between wire composition, diameter and distribution along the axis of the coil form. As part of the design process many variables are considered both with respect to the general field profile but also the manner in which the magnet will be used.

Proper design assures a robust winding while avoiding excessive
cooling losses due to excessive charging current or inadequate homogeneity. Superconducting magnets must operate below both the critical temperature and the critical field of the material from which they are constructed. Table 1 illustrates the critical temperatures and fields of the most common superconductive materials used to fabricate magnets. Figure1 shows how the capabilities of NbTi vary as a function of both temperature and field. For a superconducting magnet manufactured using NbTi, operation in the superconducting state is only possible below the surface indicated in this 3 dimensional graph.

supcondlomits

Fig1. NbTi superconducting properties.

So the limits on obtainable magnetic fields come from the materials used.

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According to this page:

The iron cores used in conventional electromagnets saturate and cease to provide any advantage at fields above a few teslas, so iron core electromagnets are limited to fields of about 2 teslas. Superconducting electromagnets can produce stronger magnetic fields but are limited to fields of 10 to 20 teslas, due to flux creep, though theoretical limits are higher. For stronger fields resistive solenoid electromagnets of the Bitter design are used. [...] Bitter electromagnets have been used to achieve the strongest continuous manmade magnetic fields on earth (up to 45 teslas as of 2011).

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You are correct. The material will saturate, so its magnetization will stop increasing. But the current also increases the magnetic field. There is no known limit to the strength of the magnetic field.

But if you increase the magnetic field to a certain point, electron and positron pairs will start being created which will be accelerated apart from eachother. This is decreasing the energy of the magnetic field untill it gets below critical energy. So in that sense there is an upper practical limit.

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  • $\begingroup$ What exactly do you mean by "practical" in that last sentence? $\endgroup$ – Emilio Pisanty Mar 8 '17 at 7:39
  • $\begingroup$ I stopped while writing that word aswell, but left it in. I did it because if you try to go above that critical level, the system starts decreasing it. I do not know if you can just power trough it, so I said practical, because working against the hill is not really that practical if it is not the main thing you are trying to achieve. :D $\endgroup$ – MaDrung Mar 8 '17 at 7:45
  • $\begingroup$ I would strongly advise against keeping that word. "Practical" implies that this can be reached in some conceivable experiment, which is not the case here. $\endgroup$ – Emilio Pisanty Mar 8 '17 at 9:04

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