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)

The discussion by Griffiths, p. 330 is seen in more detail at Amazon using the "Search inside" feature with the key word "constitutive". Likewise for Jackson, p. 14. John R. Brews 18:09, 16 December 2010 (UTC)