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According to Wikipedia, $B$ is called the

Magnetic flux density / Magnetic induction / Magnetic field,

while $H$ is called the

Magnetic field intensity / Magnetic field strength / Magnetic field / Magnetizing field.

Which of them is more fundamental? Is it meaningful to say one is more fundamental than other?

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    $\begingroup$ Define "fundamental". $\endgroup$
    – ACuriousMind ♦
    Nov 9, 2015 at 15:53
  • $\begingroup$ which is the independent quantity. $\endgroup$
    – Subhadip Roy
    Nov 9, 2015 at 16:14
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    $\begingroup$ Neither is more fundamental. The electromagnetic field is more fundamental. And four-potential is even more fundamental. See this. $\endgroup$
    – John Duffield
    Nov 9, 2015 at 20:28

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Look at the equation $\mathbf \nabla \times \mathbf H = \mathbf J_\textrm{free}$, and at the same time at $\mathbf \nabla \times\mathbf B = \mu_0 \mathbf J$. Now, $\mathbf J = \mathbf J_\textrm{bound} + \mathbf J_\textrm{free}$, and $\mathbf H = \frac1\mu_o \mathbf B - \mathbf M$, where $\mathbf M$ is called the Magnetisation. $\mathbf H$ allows me to write the Ampere's Law in terms of free current alone, and that is the thing that we control directly.

So for problems having specific symmetry I can immediately write $\mathbf H$, and from there $\mathbf B$.So in the laboratory people will talk more about $\mathbf H$ than $\mathbf B$.

And to answer your question both are fundamental.

P.S. $\mathbf B = \mu \mathbf H$, $\mathbf M = \chi_m \mathbf H$ and $\mu = \mu_0(1+\chi_m)$.

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