E&M Problem using Maxwell's Equations

shmiv
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Homework Statement



The problem statement is in the attached .png file. There are a few equations involved which would have taken a decent amount of time to type out.

Homework Equations



The Attempt at a Solution



I understand Maxwell's equations, and wrote out all 4 assuming there are no sources present. I then have 8 scalar equations that should allow me to solve for the remaining E&M field components, but I can't figure out how to relate them and arrive at a solution. Do I need to incorporate boundary conditions as well?

Thanks in advance for any and all help!
 

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Yes, you need to incorporate boundary conditions, the problem even says so.
 
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