I recommend my “crash course” in chapters 5,6,7,8 and 9 to review for this exam. (The chapter 8 review is super short, so it’s really 4 chapters, not 5.) However, this is a description of the raison d’etre of each of those chapters, i.e. what did we need from one chapter to get to where we are now (light at interfaces in media.)

Chapter 5:

  • We needed to understand Ampere’s law and magnetic fields in general so that we could use Ampere’s law which we are now using to get EM waves.

Chapter 6:

  • We needed the auxiliary field so that we could deal with magnetic fields in media, which is now allowing us to deal with waves at interfaces. We haven’t really used the vector potential again yet, but we will use this when we talk about radiation. In fact, we’ll actually make a vector potential for E-fields (notice that E is no longer divergence-less if you’re in a dynamic situation.)

Chapter 7:

  • We needed add terms to both Ampere’s law and Faraday’s law corresponding to fields changing in time so that we could get EM waves.
  • To add the term (induction) to Faraday’s law (the curl of E), we needed the notion of emf and to convince ourselves that a changing magnetic field would create one.
  • To add the term to Ampere’s law (the curl of B) we needed the concept of displacement current (that’s what Maxwell called it.)
    It is called the displacement current because \(\vec{D}\) is the displacement vector. But confusingly the displacement current arises even in a vacuum. (See page 335 in Griffiths.)
  • Then we needed to know how those terms would change in the presence of a linear medium. It turns out they don’t change Ampere’s law (curl of E) at all.
    To get Maxwell’s last equation in media (curl of H) we needed the concept of displacement current (current created in a medium when the E-field and therefore the polarization changes.) We also needed the concept of polarization current (current created in a medium when the E-field and therefore the polarization changes.)

Chapter 8:

  • All we needed here (so far) was the continuity equation, so that we could deal with waves inside conductors.

Chapter 9:

  • This is where a lot of stuff came together.
  • We derived the wave equation from Maxwell’s equations (which is why we needed the time-derivative pieces of those equations.)
  • We derived the wave equation in media (which was pretty easy because of all the pain we took in chapter 4 and 6 dealing with media)
  • Using M’s equations we figured out the relationship between E and B in a wave.
  • We figured out what happens at boundaries of conductors and dielectrics by matching boundary conditions. Notice that we needed the boundary conditions we got used to in 3 (E-fields) 4 (E-fields in matter) 5 (B-fields) and 6 (B-fields in matter.)