Understanding the Expression for a Linear EM Wave Transmission?

In summary, the conversation is about an expression in a textbook for a linear electromagnetic wave. The first question is whether the expression represents the total electric wave transmitted. The second question is about the derivation of the last expression from the second one. The speaker also requests for a source to understand this better, as there may be mistakes or missing steps in the given equations. The other person agrees and suggests seeing more of the equations to clarify.
  • #1
happyparticle
456
21
Hi,
I have an expression in my textbook that I don't really understand.
I have 2 questions regarding this expression for a linear EM wave## \tilde{\vec{E_{0i}}} = (E_{0x} \hat{x} \pm E_{0y} \hat{y}) e^{i(kz- \omega t)}##
## \tilde{\vec{E_{0t}}} = (\sum_j E_{oij} e_{pj}) \hat{e_p} ##
## \tilde{\vec{E_{0t}}} = E_0 cos \theta \hat{x} + E_0 sin \theta \cdot 0## where ##\hat{p_j} = \hat{x}##

First of all, is it the total electric wave transmitted? and secondly, can someone explain me how we get the last expression from de second?
 
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  • #2
Can you give a source where this came from? It looks like class notes where they may have made a mistake and/or left out a step or two.
 
  • #3
Yes, what @Charles Link said. Those subscripts are really confusing. We need to see more.
 
  • Like
Likes Charles Link

FAQ: Understanding the Expression for a Linear EM Wave Transmission?

1. What is a linear EM wave?

A linear EM wave is a type of electromagnetic wave that propagates in a straight line and has a constant amplitude and frequency. It is characterized by a sinusoidal waveform and can travel through a vacuum or a medium such as air or water.

2. How is a linear EM wave transmitted?

A linear EM wave is transmitted through the oscillation of electric and magnetic fields. These fields are perpendicular to each other and to the direction of propagation. The changing electric field creates a changing magnetic field, which in turn creates a changing electric field, and this cycle continues as the wave travels through space.

3. What are the properties of a linear EM wave?

A linear EM wave has several properties, including wavelength, frequency, amplitude, and velocity. The wavelength is the distance between two consecutive peaks or troughs of the wave, and the frequency is the number of cycles per second. The amplitude is the maximum value of the electric or magnetic field, and the velocity is the speed at which the wave travels through space.

4. How does a linear EM wave interact with matter?

A linear EM wave can interact with matter in several ways. It can be reflected, transmitted, or absorbed by different materials. The amount of interaction depends on the properties of the material, such as its conductivity and permittivity. In addition, the angle of incidence and the polarization of the wave can also affect the interaction.

5. What are some practical applications of linear EM waves?

Linear EM waves have numerous practical applications in our daily lives. They are used in communication systems, such as radio, television, and cell phones. They are also used in medical imaging technologies like MRI and in industrial processes such as heating and welding. Additionally, linear EM waves are essential in the study of astronomy and the exploration of outer space.

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