# TEM mode propagation between 2 infinite conductor plates

1. Feb 12, 2015

### fluidistic

1. The problem statement, all variables and given/known data
I am trying to solve a problem from Jackson's book (in chapter 8). I must describe the propagation of a TEM mode through a transmission line that consists of two infinite conductor plates that are parallel to each other and separated by a distance a. There's a dielectric between the 2 plates.

At first I did not know how to start the problem. Maybe solve the wave equation with boundary conditions that $\vec E$ must be perpendicular to the conductor surfaces and $\vec B$ must be parallel to it and both fields should have no component in the z direction, the direction of propagation. On the top of this, since it's a TEM, Jackson's demonstrate that in a hollow cylinder the fact that $E_z$ and $B_z$ vanish implies that these fields satisfy electrostatics Maxwell equations and I believe it is also the case for the exercise I'm dealing with. This is also confirmed by page 14 of http://www.ece.msstate.edu/~donohoe/ece4333notes3.pdf for the particular set up I'm facing in this problem.

2. Relevant equations
Not sure...

3. The attempt at a solution
Following the document linked above I reach that $\vec E=-\frac{V}{d}e^{-ikz}\hat y$ and $\vec H=\sqrt{\frac{\varepsilon}{\mu}}\frac{V}{a}e^{-ikz}\hat x$.
So I see no propagation, no time dependence... However in the document I linked above one read
which confuses me even more. How come there is a current in the plates? They seemed to act like a capacitor to me and as far as I know there is no current in the plates... What I am missing?

I've also found another solution to the problem but it did not convince me since the guy assumes time dependence of the fields and for some unknown reason to me, he assumes from the start that the current in the plates if of the form $\vec K=(z,t)=K_0\mu e^{i(kz-\omega t)}\hat x$. See http://www-personal.umich.edu/~pran/jackson/P506/P506W02HW02.pdf.

So which answer is correct? Thank you.

2. Feb 17, 2015