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If I use a solenoid of $ h = 0.1\, \mathrm{m}$, with a current of $ I = 30\, \mathrm{A}$ , with $62$ turns and an iron core of permeability $\mu = 0.25$, then it will give me a magnetic field of:

$$B = \frac{\mu \times I \times N}{h} = 4650 \, \mathrm{T}.$$

That makes no sense. Did I just break the Guinness record with a home experiment?

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  • $\begingroup$ It's really the correct permeability according to Wiki: en.wikipedia.org/wiki/… $\endgroup$ Commented Jan 19, 2022 at 4:06
  • $\begingroup$ Permeability you took here might be incorrect or it might be the relative Permeability. I think it's much more easy to understand that physically it's not possible for a solenoid of length jusr 0.1 meter and second of all the equation which you've used is only for the solenoid with the condition where radius of solenoid is << length of solenoid and you haven't specified the radius of the solenoid as well so it is difficult to conclude anything, But hey!!. And This is not possible for a normal solenoid to give you this massive amount of magnetic field strenght... $\endgroup$ Commented Jan 19, 2022 at 4:58

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Your value of the permeability is not realistic. The real magnetic permeability of iron is complicated and depends on the geometry, the crystal structure, the purity, and the history of a particular sample. A typical value of the relative permeability for good everyday iron would be $\mu_{r}\sim 1000$. This makes the absolute permeability roughly $$\mu=\mu_{r}\mu_{0}=\mu_{r}\left(4\pi\times 10^{-7}\right) \,\mathrm{H}\cdot\mathrm{m}^{-1}\sim10^{-3}\,\mathrm{H}\cdot\mathrm{m}^{-1}.$$ For exceptionally pure and ideally machined iron, it is indeed possible to achieve permeabilities hundreds of time higher. However, it takes very little impurity to spoil this; the value you mention was for 99.95-percent-pure iron in the absence of reactive oxygen. Moreover, it is probably not really possible to maintain that effective permeability for large samples like your $10\,\mathrm{cm}$ example.

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  • $\begingroup$ Makes more sense now. But I still get 23 Teslas which seems dangerous to be nearby, no? $\endgroup$ Commented Jan 19, 2022 at 4:10
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Another issue is that this equation seems to assume same permeability through the whole space. But solenoid's core is not closed, not a loop, magnetic flux has to go out in empty space on the outside of the coil. So effective permeability will be (much?) less than permeability of the core material.

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