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palpa
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Homework Statement
a) Assuming the presence of sources (J flux density) and (p charge density) , write out Maxwell’s equations in the time domain in terms of and only for a lossless, but inhomogenous medium in which
ε = ε(r) , μ = μ(r).
b) Derive the vector differential equation (wave equation) satisfied by E(r,t) in a source-free, lossless, inhomogenous medium.
(There are lines on the "r"s indicating that they are position vectors)
Homework Equations
maxwell's equations and the equations that relate D&E and B&H (I am not sure about which forms should be used)
The Attempt at a Solution
I am blowing my mind over this but couldn't see what is being meant by inhomogeneous medium. Obviously I am not asked for the inhomogeneous wave equation (it is not in the curriculum), so I thought this was about anisotropic medium where ε&μ are different for different positions, but when I read about it, I've encountered lots of stuff I haven't even heard about (like tensors).
Please give me a starting point. D=εE , but if ε is not constant, it is not a scalar. If it's not a scalar, how is D=εE true? Or is ε a tensor and since it is a matrix I should treat it like a scalar? Then what is the difference of the answer from constant ε&μ wave equation?
Please help I am desperate.