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

[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

 

[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.

 

[rude man]

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

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.