# Magnetic field and magnetic field intensity and magnetisation intensity ($B$, $H$, $I$) [duplicate]

I am really confused between magnetic field (B)and magnetic field intensity(H) and magnetisation intensity(I) Please can someone explain them to me and these formula H=B/μ -I, I=M/V, I am a high school student so i may not be able to understand tensors and stuff which a lot of other articles i read used. I also don't yet know the analogies of these with there electrostatic counter parts.

The magnetization (intensity) is defined as the magnetic dipoles $$\mathbf{\mu}$$ per unit of volume:

$$\mathbf{M} = \frac{\sum \mathbf{\mu}_i}{\Delta V} \hspace{10pt} [Am^{-1}]$$

The magnetization is material related. Some materials have magnetic dipoles and thus magnetization whereas others have not.

The magnetic field is $$\mathbf{H}$$ with units $$[Am^{-1}]$$. The field can be nonzero in a material but also be nonzero in vacuum (whereas the magnetization is zero in vacuum because there are no dipoles). This magnetic field is also the field present in an electromagnetic wave for example.

The magnetic induction is defined as the sum of the magnetic field and magnetization:

$$\mathbf{B} = \mu_0 (\mathbf{H} +\mathbf{M})\hspace{10pt} [T]$$

So, the magnetic induction can be seen as a quantity that quantifies the net magnetic strength at a specific point in space. It takes into account the magnetic effects originating from fields ($$\mathbf{H}$$) and from the materials themselves ($$\mathbf{M}$$).

• But in many places I've seen that B is used to denote magnetic field like in the biot savartz law. And also if we talk about magnetic material kept in an external field, the magnetic field inside it is B=μ(H+M), what is the field outside the material as now due to the external field, the material also generates it's own magnetic field. Dec 3 '19 at 12:44
• And,by the way this is a great answer, but I still can't get my head around this topic, any suggestions what I should do? Dec 3 '19 at 12:46
• It is indeed a confusing topic as people often use both B and H for "magnetic fields". In the SI-unit system, H is the magnetic field in [A/m] and B is the magnetic flux density or magnetic induction in [T]. Dec 3 '19 at 13:22
• The magnetic induction outside will be: $B=\mu_0 (H_{tot}+M) = \mu_0 (H_{ext}+H_{stray}+0) = \mu_0 (H_{ext}+H_{stray})$. Outside, the magnetization is zero. The field generated by the magnetization is called the stray field $H_{stray}$. The magnetic field outside is $H_{ext}+H_{stray}$. Dec 3 '19 at 13:23
• Here is another related question to this topic with a good answer: physics.stackexchange.com/questions/517351/…. Maybe this will also help you. Dec 3 '19 at 13:25