# Demagnetization field of a prism magnet

I am studying some magnetism, and i am curious about bar magnets.

Lets say you have an uniform prism magnet of Iron for example. How would you calculate the demagnetization field H which the bar magnet produces? As I understand, first you need the magnetization M which is the magnetic moments per volumen. But then what ? Or would you apply and external field to the bar magnet and see how it reacts, if this is the case, how does this work ?

If you know M then H is just $\frac{M}{\chi_m}$ where $\chi_m$ is the magnetic susceptibility. This only holds for paramagnets and diamagnets, however. In the case of a ferromagnetic material like iron, you would have to refer to the hysteresis curve. If you know the net (= applied+induced) magnetic field B in the material, then you can use any of these relations
\begin{align*} H=& \frac{B_{net}}{\mu}\\ H=& \frac{B_{applied}}{\mu_0}\\ H=& \frac{B_{net}}{\mu_0}-M\\ H=& \frac{B_{applied}+\mu_0M}{\mu}\qquad{(\because B_{induced}=\mu_0M)} \end{align*}where $\mu=$permeability.