Because dumped and undumped solutions cannot equal for all t. Therefore, continuous tangential electric field is not guarateed in the boundary of both media.
I need the field distributions. A transmission line model won't fit because I'm looking for TE and TM modes on a coaxial cable, semi-infinite, with 2 dielectrics: one lossy and the other lossless. And I need distributions of field because I need to find the best way to place some receivers for a...
I insist because A dumped wave does not solve mawell equation for lossless media. Besides, I already tried using time harminic waves to solve my problem. However, I can't solve the proble using real number frequencies. I must be doing something wrong or simply it is not solvable on frequency domain
actually, confused me a lot!
Andy, my apologies, but a damped wave cannot be a solution for wave equation in the lossless media. Its math now, not physics. How can a dumped wave be a solution for \partial^2 E / \partial x^2 = \mu \epsilon \partial E / \partial t
Ok, i think I am not explaining myself clearly. I tried to simplify the problem, but I'll post it entirely here, because I need help. It's for my msc program.
I have a structure made by coaxial cylinders of radius a < b. The cylinders are PEC material (perfect electrically conductor)...
That's perfect! for a time harmonic wave. Take a closer look, and you'll find out that your waves are still time harmonic (exp{jwt}). My question is about time domain because I am working with transients. Books assume every wave in the world can be represented by a fouries series expanded using...
You have a point. However, since I'm assuming no sources, it has no meaning in saying "the incident field is coming from a lossy medium". Moreover, a decaying wave cannot solve Maxwell equation \nabla^2 E_x = \mu \epsilon \partial^2 {E}_x / \partial t^2 - the equation for the lossless media.
I'm keeping a conduction current, not a source current. There's a difference. Anyways, you are wrong: The tangential electric field is discontinuous if, and only if, there is an impressed magnectic current, which is not the case. It has nothing to do with electric charge density. Actually...
I was wrong, the problem is yet not solved.
The question is about boundary conditions in the interface of separation of 2 media: one is lossy and the other is lossless.
In the lossless media, the wave is non-decaying. In the lossy media, the wave is decaying in time.
Since I am assuming...
Sure it can, but it doesn't help answering my question. Diving a little deeper in book "Advanced Engineering Electromgnetics" - Constantine A. Balanis, I ran into the continuity equation, which states:
\nabla \cdot (J_i + \sigma E) = -\dot{q_{ev}}. Therefore, since \sigma is not null, there...
actually, equation is:
\nabla^{2} E = \mu \sigma \frac{\partial E}{\partial t} + \mu\epsilon \frac{\partial^{2} E}{\partial t ^{2}}
Suppose there is only E_{x} , so:
E = \hat{a}_{x} E_{x}
and equation can be rewriten as
\nabla^{2} E_x = \mu \sigma \frac{\partial...