Trying to understand Maxwell's equation in a medium

[mikeyBoy83]

So I believe I understand Maxwell's equation in vacuum pretty well and I feel like I understand them in different medium when I read in a textbook, but when I have to apply it to exercises I get thrown off quite a bit. For example, I cam across a PhD qualifying exam that had split Euclidean space between two regions with vacuum and a region of dielectric constant e1. So the region with dielectric existed below the xy-plane and the region without existed above the xy-plane. It then asked what the components of the equations were in the two regions. I didn't even know where to begin.

What are some good resources for studying dielectrics and Maxwell's equations in media? If you have any good suggestions or no how to explain the theory in a relatively simple manner that would help too. Thanks in advance!

 

[RUber]

I worked out of Balanis - Advanced Engineering Electromagnetics. It has been a good reference, especially for the applications you mentioned.
Most of these problems hinge upon the fact that waves propagate at a speed determined by the material parameters. After that, you enforce continuity requirements for when waves cross boundaries, and you move on from there.

 

[vanhees71]

I'd recommend the Feynman Lectures Vol. II.

 

[mikeyBoy83]

Yeah, I will try those first. I can't believe I used "no" in place of know. . . Sheesh I must have been really tired when I typed this up. Thanks for the references guys!