How Does the Divergence of Magnetic Field Relate to Magnetizing Fields?

[hotel]

Hi
I am trying to derive the relation between magnetic field strength in materials and magnetizing field from the $\mathbf B$ field. More exactly, my question is:

how do we get this expression

<br /> $\nabla \centerdot \mathbf H = - \nabla \centerdot \mathbf M$ \\ <br />

knowing

<br /> $\nabla \centerdot \mathbf B = 0$ \\ <br />

and

<br /> $\mathbf B=\mu_0(\mathbf H + \mathbf M )$ <br />
?

Anyone can guid me how the first equation is related to the 2nd and 3rd equations?

thanku

 

[inha]

\nabla \cdot B=\nabla \cdot {\mu}_0(H+M)=0

Do you get the idea now?

 

[hotel]

I 'm not sure !?

but how do we get from this:

\nabla \cdot B=\nabla \cdot {\mu}_0(H+M)=0

to this:

\nabla \cdot H= -\nabla \cdot M

I can only see you have replaced B !

Or maybe you want me to think like this :
\nabla \cdot H=\nabla \cdot {\mu}_0H+{\mu}_0M
\nabla \cdot H=\nabla \cdot {\mu}_0M
assuming for a very small volume of material ?

or am I totally misunderstanding !?

 

[inha]

\nabla \cdot {\mu}_0(H+M)=0

divide \mu_o out. you can do that since it's just a constant. then you have

\nabla \cdot H + \nabla \cdot M=0

which is what you're looking for once you move the M-term to the other side of the eq.