Talk:Maxwell equations

I don't see anything here about the question of magnetic monopoles. Peter Jackson 12:01, 17 November 2008 (UTC)

Classically there are no magnetic monopoles, cf. first (magnetic) law and third (electric) law . Where the third law has a charge ( = monopole) on the right-hand side, the first law has zero. When you are not satisfied with the text about this point, please go ahead change it, CZ is a wiki. --Paul Wormer 14:25, 17 November 2008 (UTC)

I'm not an expert on this, & wouldn't know what answers to put in. All I can do without research is ask questions, eg did Maxwell consider the question? Peter Jackson 16:06, 17 November 2008 (UTC)

Very early on (around 1780) it was clear that cutting magnets into two pieces always gave two poles, a North pole and a South pole, so Gauss around 1830 and Maxwell around 1870 definitely knew that a magnetic monopole was never observed. As far as I know there is no deeper reason known for the non-existence than the empirical fact that it has never been observed. --Paul Wormer 17:00, 17 November 2008 (UTC)

Quite so. I was hoping someone with more knowledge on the point might add it if I pointed out the issue. Peter Jackson 11:57, 18 November 2008 (UTC)

Constitutive relations

Although the usage of the article at present is sometimes found, the equations:

$\mathbf {D} \equiv \epsilon _{0}\mathbf {E} +\mathbf {P} ,\qquad \mathbf {H} \equiv {\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} ,$

are not normally what is called constitutive relations. Rather, they are (as indicated here) definitions of the fields D and H that appear when materials are present.

Rather, the constitutive equations more usually are taken to be formulas that allow elimination of D and H, for example, by the introduction of permittivities or permeabilities:

$\mathbf {D} =\epsilon \mathbf {E} ;\qquad \mathbf {H} ={\frac {1}{\mu }}\mathbf {B} \ ,$

and the related susceptibilities:

$\mathbf {P} =\chi _{e}\mathbf {E} \ ;\qquad \mathbf {M} =\chi _{m}\mathbf {H} \ .$

Some examples of this usage are Sihvola and Griffiths, p. 330, Jackson, p. 146. John R. Brews 17:52, 16 December 2010 (UTC)