Maxwell's equations for TEM mode

[Young_Scientist23]

Dear All,

I'm confused after reading of some chapter in a book, in which equations related to TEM mode have been derived. I want to prove mathematically, that Electric and Magnetic fields are ortogonal to each other. Thus, I use well known Maxwell equation:

$$\nabla \times \overrightarrow{E} + \frac{\partial \overrightarrow{B} }{\partial t} = 0$$

Due to fact, that the TEM mode is considered i.e. $\overrightarrow{E}$ varies only with $z$ plane ( $\frac{\partial \overrightarrow{E} }{\partial x} = \frac{\partial \overrightarrow{E} }{\partial y} = 0$)

I calculate the following relation for TEM:

$$\overrightarrow{i}(-\frac{\partial E_y}{\partial z}) + \overrightarrow{j}(\frac{\partial E_x}{\partial z}) + \overrightarrow{i}(\frac{\mu \partial H_x}{\partial t}) + \overrightarrow{j}(\frac{\mu \partial H_y}{\partial t}) = 0$$

whereas in mentioned book is:

$$\overrightarrow{j}(\frac{\partial E_x}{\partial z}) + \overrightarrow{i}(\frac{\mu \partial H_x}{\partial t}) + \overrightarrow{j}(\frac{\mu \partial H_y}{\partial t}) = 0$$

I'm wondering what happens with $\overrightarrow{i}(-\frac{\partial E_y}{\partial z})$. I've made something wrong or there is some issue in the book ?

Regards,
E.

 

[Paul Colby]

Well, the book you're looking at or at least a description of the geometry might help.

One suggestion, $\text{TEM}_{10}$ modes in a rectangular guide may be written or viewed as the sum of two plane waves. Each is the reflection of the other at the guide angle.

 

[Meir Achuz]

1. What book?
2. What kind of wave guide?
3. Your equations look like they are for a rectangular wave guide, but a TEM wave needs two separate surfaces.
4. The book could just be considering a wave polarized in the x direction.