Why is the magnetic intensity in a material determined only by the external sources even if the material is magnetized?

Question

The following text is from Concepts of Physics by Dr. H.C.Verma, from the chapter "Magnetic Properties of Matter", page 281, topic "Magnetic Intensity $H$":

Whenever the end effects of a magnetized material can be neglected, the magnetic intensity due to magnetization is zero. This may be the case with a ring-shaped material or in the middle portion of a long rod. The magnetic intensity in a material is then determined by the external sources only, even if the material is magnetized.

Earlier, I came across the following formula: $$\vec H=\frac{\vec{B}}{\mu_0}-\vec I$$ where, $\vec H$ is the magnetic intensity or magnetizing field intensity, $\vec B$ is the resultant magnetic field (vector sum of applied magnetic field and the magnetic field due to magnetization) and $\vec I$ is the intensity of magnetization (magnetic moment per unit volume).

However, I don't understand why the magnetic intensity due to magnetization is zero when there is no significant end effects as said by the author. I thought resultant magnetic field at a particular point inside a material to be equal to the vector sum of the external magnetic field applied and the magnetic field due to magnetization. But this statement is opposite of what I understood.

It would be helpful if you could explain the above quoted statement. Why is the magnetic intensity in a material determined only by the external sources even if the material is magnetized?

Answer 1

I am not sure I have fully understood your description. However I think I can answer your last question.

For static fields, the set of magnetic Maxwell equations is: $$ \begin{align} \nabla \cdot {\bf B} &= 0 \\ \nabla \times {\bf H} &= {\bf j_{ext}}, \end{align} $$ which, for a linear medium, i.e. a medium characterizd by a linear relation between ${\bf H}$ and ${\bf B}$: $$ {\bf H(r)}=\frac{{\bf B(r)}}{\mu} $$ become $$ \begin{align} \nabla \cdot {\bf H} &= 0 \\ \nabla \times {\bf H} &= {\bf j_{ext}}. \end{align} $$ On the other hand, in the vacuum (i.e. in the absence of magnetization), ${\bf H(r)}=\frac{{\bf B(r)}}{\mu_0}$ and the resulting equations for ${\bf H}$ is the same as for the case with the medium. In both cases, the external current acts as the source of the field. Of course, there is a difference in the two cases, but it is confined to the different values of ${\bf B(r)}$.

Answer 2

The vector $\vec{H}$ is called the "Magnetizing field intensity",which is actually the measure of the intensity of the magnetizing external field.And the external field is actually indifferent to whether is a magnetization or not. What is affected is the "resultant magnetic field" or the vector $\vec{B}$.