Is Gauss' Law Applicable to Dynamic Charges and All Surfaces?

[htg]

The issue is that textbooks (e.g. Griffiths: Introduction to electrodynamics) say that divergence of magnetization at the end of a magnet is infinite.

 

[Born2bwire]

The issue is that textbooks (e.g. Griffiths: Introduction to electrodynamics) say that divergence of magnetization at the end of a magnet is infinite.

Where in Griffiths does it say this?

 

[jtbell]

Third edition, page 276:

since M and H are [in linear media] proportional to B, does it not follow that their divergence, like B's must always vanish? Unfortunately, it does not: at the boundary between two materials of different permeability the divergence of M can actually be infinite. For instance, at the end of a cylinder of linear paramagnetic material, M is zero on one side but not on the other.

$\nabla \cdot \vec M$ and $\nabla \cdot \vec H$ being infinite simply reflects the idealization of the boundary as being perfectly "sharp," with M and H changing "instantaneously" as you cross the boundary.

 

[Born2bwire]

Third edition, page 276:



$\nabla \cdot \vec M$ and $\nabla \cdot \vec H$ being infinite simply reflects the idealization of the boundary as being perfectly "sharp," with M and H changing "instantaneously" as you cross the boundary.

Yeah, the dirac delta that results in the divergence due to an discountinuous boundary condiion. But that is still ok for the reasons that you, jtbell, specified earlier. Gauss' Law makes constraints on the B field, not the H and M so the fact that these quantities are not always divergence free is not in contradiction with the law.

 

[htg]

At the end of section 6.4.1 (susceptibility and permeability) - at least in my Polish translation.

 

[htg]

Third edition, page 276:



$\nabla \cdot \vec M$ and $\nabla \cdot \vec H$ being infinite simply reflects the idealization of the boundary as being perfectly "sharp," with M and H changing "instantaneously" as you cross the boundary.

It does not make much sense to pretend that we think matter is continuous, especially because here it leads to completely false conclusions.

 

[hercules68]

Gauss's law is verified experimentally for static charges, how is it verified for dynamic charges ?