- #1

Young_Scientist23

- 11

- 0

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.

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.

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