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yungman

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I am referring specificly to page 273 6.3.2 A Deceptive Parallel in the "Introduction to Electrodynamics" 3rd edition by David Griffith that I am sure most of you have. The book said:

1) [itex] \nabla \cdot \vec B = 0 \hbox { does not imply } \nabla \cdot \vec H = 0 [/itex]

2) [itex] \nabla \cdot \vec H = \nabla \cdot \frac{1}{\mu_0} \vec B - \nabla \cdot \vec M = -\nabla \cdot \vec M [/itex].

[itex]\hbox { 3) Only } \nabla \cdot \vec M = 0 \Rightarrow \vec B = \mu_0 \vec H [/itex].

My questions are:

1) When is [itex] \nabla \cdot \vec M \hbox { not equal to } 0 [/itex] ?

2) Is it true that all diamagnetic and paramagnetic material, [itex] \vec M \hbox { is parallel to } \vec B_{ext} [/itex] ? Or the material has to be linear and isotropic on top of dia and paramagnetic?

3) Sounds like to me only the ferromagnetic material that [itex] \vec M [/itex] is not parallel to [itex] \vec B_{ext}[/itex] until all domains are lined up with the external magnetic field?

4) what are the example of non-isotropic material?

1) [itex] \nabla \cdot \vec B = 0 \hbox { does not imply } \nabla \cdot \vec H = 0 [/itex]

2) [itex] \nabla \cdot \vec H = \nabla \cdot \frac{1}{\mu_0} \vec B - \nabla \cdot \vec M = -\nabla \cdot \vec M [/itex].

[itex]\hbox { 3) Only } \nabla \cdot \vec M = 0 \Rightarrow \vec B = \mu_0 \vec H [/itex].

My questions are:

1) When is [itex] \nabla \cdot \vec M \hbox { not equal to } 0 [/itex] ?

2) Is it true that all diamagnetic and paramagnetic material, [itex] \vec M \hbox { is parallel to } \vec B_{ext} [/itex] ? Or the material has to be linear and isotropic on top of dia and paramagnetic?

3) Sounds like to me only the ferromagnetic material that [itex] \vec M [/itex] is not parallel to [itex] \vec B_{ext}[/itex] until all domains are lined up with the external magnetic field?

4) what are the example of non-isotropic material?

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