# Is this a correct way of finding magnetic field of a magnet created with Wasilewski's method?

$$\quad$$ Wasilewski's method (Or the method that could be seen in Dr Stone episode 9) consists of piece of iron being struck by a lightning, which then magnetises it. Let's say, we have a cylindrical piece of iron of length $$d$$ and radius $$r$$. Then we insulate the iron and wrap a copper wire of length $$l$$ and cross section area $$S$$ around the iron $$n$$ times. Then we let the lightning strike it. Now comes the calculation.

We have some given value of lightning voltage, so the current passing through the wire will be$$I=\frac{U}{R}=\frac{US}{l\rho}$$ $$\rho$$ being resistivity of copper. Thanks to the Ampere's law we know, that magnetic field inside a solenoid is$$B=\frac{\mu In}{d}=\frac{\mu USn}{dl\rho}$$ $$\mu$$ being magnetic permeability of iron. Then as a last step we can express length of the wire as $$l=2\pi rn$$, making the magnetic field of a our iron magnet$$B=\frac{\mu US}{2\pi d\rho}$$

Now I don't know, if this really is correct. Please, if I'm wrong, tell me where is my mistake. And in case this is correct, I know the field I just calculated is just the field inside of the magnet, not outside of it, but considering putting two same magnets very close to each other with opposite poles, the field between them should be around the same as the field inside of them, am I correct?

* There is one problem with your method, even in the static case. Ferromagnetic materials don't have a "permeability" in the sense that you don't have $$H = \frac{1}{\mu} B$$ for such materials. Rather, $$H$$ is a non-linear function of $$B$$.