E&M Question -- Maxwell's Equation in matter reduce to Maxwell's equation in a vacuum....

[ParticleGinger6]

Homework Statement:

Maxwell's Equation in matter reduces to Maxwell's equation in vacuum if polarization and magnetization are zero?

Relevant Equations:

They can be found in the attached photo

I do not know where to start.

 

[robphy]

How are polarization (i.e. the Polarization Vector Field) and magnetization (i.e. Magnetization Vector Field)\\ related to the vector fields $\vec D$ , $\vec E$, $\vec B$, and $\vec H$?

 

[ParticleGinger6]

@robphy so i found the equations D = epsilon*E and H = (1/mu)*H where epsilon = epsilon(not)*(1+Xe) and mu = mu(not)*(1+Xe). I think if I use that convert D into terms of P which would look like P = D - epsilon(not)*E and H = B/(mu(not)*(1+Xe)). From there you can get Magnetization from M = Xm*H

Am I on the right track

 

[robphy]

Yes... but use $\epsilon_0$ and $\mu_0$ instead of the $\chi$s.

 

[ParticleGinger6]

@robphy I believe I figured it out. So by using D = epsilon(not)E + P and H = B/mu(not) - M I was able to get to
dell * E = rou/epsilon(not) and dell cross B = mu(not)*J + mu(not)*epsilon(not)*(curly(d)*E/curly(d)t) for part a
Then for part b
I used P = epsilon(not)*X*E to get dell*E = rou/epsilon(not)
I used M = Xm*H to get dell cross B = mu(not)*J + mu(not)*epsilon(not)*(curly(d)*E/curly(d)t)
Both assuming mu approaches mu(not) and epsilon approaches epsilon(not)