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

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?

• Did you understood the question, you have posted?, if yes then can you please explain the answer of your own question? Please if possible avoid complex equations, as i am just a beginner in magnetism. I can't post the same question as it would become duplicate – maverick Jul 16 at 11:03
• Can you Please help? If you understood the quote by HC Verma, can you help me understand it, The answer given below is beyond my scope for now , so please help.. – maverick Jul 16 at 14:34
• @maverick: I have not understood the answer by Giorgio mainly because I haven't studied vector calculus in detail. See whether this conversation I had with John Rennie in the chat is useful. If not you can also chat with him in this room. He is mostly available from 10 a.m. IST to 4 p.m. IST. – Guru Vishnu Jul 16 at 14:51
• If you're interested in learning further, I came to know that the book Introduction to Electrodynamics by David Griffiths is good place to start vector calculus. I probably might answer my question after learning it fully. But it will be only after my exams. – Guru Vishnu Jul 16 at 14:57
• I am sorry @GuruVishnu, but i am really a newbie to magnetism in class 12 the book you have mentioned will not help for now, time is also running out, with exams just knocking at my door, But thank you for the suggestion, for now my standard books for concepts are HC Verma and DC pandey they help me out in most cases, and iam sure i will find some answer to this one as well, Thank you for your time – maverick Jul 16 at 15:37

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 $${\bf B(r)}$$.
• Thank you for your answer. Re: "I am not sure I have fully understood your description. However I think I can answer your last question." Could you please tell how to improve my question? The entire description was for the "last question". Further, may I know why is there no intensity of magnetization term ($\vec I$ - magnetic moment per unit volume) in in your answer unlike $\vec H=\frac{\vec B}{\mu_0}-\vec I$ as given in the question? – Guru Vishnu Feb 28 at 8:17
• @GuruVishnu Indeed, I answered your last question without mentioning magnetization, because I did not understand why you say that the magnetic intensity due to magnetization is zero. I explicitly mentioned a linear medium, where magnetization intensity is proportional to $B$, ending up with $\vec H=\vec B/\mu$, where $\mu$ is the magnetic permeability of the material. The linear relation allows to write equations containing $\vec H$ only, but does not imply that intensity of magnetization is zero. – GiorgioP Feb 28 at 9:17
• "magnetic intensity due to magnetization is zero" - Sorry. I didn't say that. It was quoted from my textbook. Further, even I have trouble in understanding the same statement and is the reason for posting this question here. I can understand your example. But is there any reason for using permeability of the material $\mu$ over permeability of vacuum $\mu_0$? I think this might contain the answer to my previous comment. – Guru Vishnu Feb 28 at 10:32
• @GuruVishnu Yes, there is a reason. For linear media, magnetization ca be absorbed into a linear relation between $\vec B$ and $\vec H$ with a permeability different from that of vacuum. – GiorgioP Feb 28 at 12:28