I Understanding the Expression for a Linear EM Wave Transmission?

AI Thread Summary
The discussion centers on clarifying an expression for a linear electromagnetic wave transmission found in a textbook. The user questions whether the expression represents the total electric wave transmitted and seeks an explanation for deriving one expression from another. Confusion arises from the notation and subscripts used in the equations, indicating a need for further clarification. Participants suggest that additional context or examples are necessary to fully understand the derivation and application of the expressions. Overall, the conversation highlights the complexity of electromagnetic wave equations and the importance of clear notation in understanding them.
happyparticle
Messages
490
Reaction score
24
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?
 
Physics news on Phys.org
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.
 
Yes, what @Charles Link said. Those subscripts are really confusing. We need to see more.
 
  • Like
Likes Charles Link
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top