# Dynamic Maxwell equations, uniqueness theorem, steady-state response.

1. Jun 6, 2012

### eliotsbowe

Hello, I'm trying to make a sort of "system theory approach" to dynamic Maxwell's equations for a linear, isotropic, time-invariant, spacely homogeneous medium.

The frequency-domain uniqueness theorem states that the solution to an interior electromagnetic problem is unique for a lossy medium; but if the medium is lossless, then there can be "resonant solutions".

The above-mentioned unique frequency-domain solution should return, in the time-domain, the steady-state response of the electromagnetic field to a sinusoidal source.
What do resonant solutions return in the time-domain?
Let the electromagnetic field be forced, in a lossy medium, at a resonance frequency: would the solution be unique?

If the phasor-domain uniqueness theorem returns the steady-state response, does the time-domain one return the zero-input response as well?

2. Jun 6, 2012

### Jano L.

Your questions is not entirely clear to me. What book are you studying?

If the question is what would happen in a medium that has no macroscopic energy loss, the answer would be that the oscillations of the medium are not damped. This would mean the initial conditions on the state of the field would be important for the field in later instants, i.e. the particular solution will not be total electromagnetic field - there will be also homogeneous part due to proper oscillations of the medium.

3. Jun 10, 2012

### eliotsbowe

I think I was too confused on the matter, perhaps I couldn't ask my questions in a plain way.
Solution: I asked the professor himself. Thanks anyway!