# Definitions of $\vec{B}$ and $\vec{H}$

From here, I have got the definition of $\vec{H}$. However even in wikipedia and other sites, I cannot find a definition for $\vec{B}$ which shows its similarity with $\vec{H}$.

Similarity: I know for free currents, $\vec{B}$ and $\vec{H}$ are same. I also know outside the magnet, for bound currents, $\vec{B}$ and $\vec{H}$ are same.

What is the definition for $\vec{B}$ whic makes it so much similiar to $\vec{H}$?

• $H=\frac{B}{\mu_0}-M$ where $M$ is the magnetization. – Aaron Stevens Sep 14 '18 at 6:10
• I see... I understand the formula.... But what would be the physical interpretation of $\vec{B}$.... In other words, when we have a useful quantity "$\vec{H}$" in the first place, what is the need of defining another quantity called $\vec{B}$ – N.G.Tyson Sep 14 '18 at 8:47

I would say the more "fundamental" field is actually the magnetic field $\vec B$. The definition of $\vec H$ from this is then
$$\vec H=\frac{\vec B}{\mu_0}-\vec M$$
Where $\vec M$ is the magnetization of the medium your magnetic field is in.
Both are useful depending on the context. Since the magnetization in free space is $0$, $\vec B$ is more useful when looking at fields in a vacuum or media where magnetization can be neglected. $\vec H$ is more useful when your magnetic field is in some medium where a net magnetization arises.