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?
Best Answer
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.