# Why are P/M and D/H defined oppositely in Electromagnetism

1. May 18, 2015

### I<3NickTesla

The definitions of D and H are:

$D=\epsilon_0 E+P$
$H=B/\mu_0-M$

$P=\epsilon_0 \chi E$
$M=\chi H$

I was wondering, if E and B are the fundamental field relating to all charges/currents, why is the definition of the polarisation the opposite for each of them? So why is H in the definition of M and not B, when B is the actual physical field.

Thanks

2. May 18, 2015

### TSny

You can trace the difference in sign to the relations

$\vec{\nabla} \cdot \vec{P} = -\rho_{bound}$ and $\vec{\nabla} \times \vec{M} = +\vec{J}_{bound}$

where $\vec{P}$ and $\vec{M}$ are electric and magnetic polarization vectors.

3. May 19, 2015

### rude man

I would venture that H is more fundamental than B, in the sense that B is H modified by magnetic material, just as D is E modified by dielectric material.
E.g. you have a solenoid with current thru it: the B field is one thing if the core is air and another if the core is iron. But H does not change. Ampere's law is most simply stated as ∫H ds = I.

But that's just a venture.