# How much time does it take magnetization to appear, after turning on a magnetic field?

When a magnetic field $${\bf H}$$ is turned on from zero, a piece of material, not previously magnetized, exhibits a magnetization $${\bf M}$$ due to $${\bf H}$$.

According to $${\bf M} = \chi {\bf H}$$, this would happen instantaneusly. But that's hard to believe, because magnetic moments, inside the bulk of the material, should take some time to turn around themselves.

Suppose $${\bf H}$$ is varying with time, such as $${\bf H}\propto e^{-i\omega t}$$. If $$\omega$$ is high enough, a temporal phase shift between $${\bf M}$$ and $${\bf H}$$ should occur, due to the time taken by the magnetic dipoles to turn around.

So, what is the frequency range where $${\bf M} = \chi {\bf H}$$ should be used, as if $${\bf M}$$ would follow $${\bf B}$$ instantaneously?

• There is a distinction between the ambient field and the field inside the material exposed to the ambient field. $\textbf{M}=\chi\textbf{H}$ refers to the $\textbf{H}$ field inside the material. – Ben Crowell Nov 27 '18 at 1:22