Electromagnetic wave equation - phase and amplitude

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Discussion Overview

The discussion revolves around the derivation and interpretation of the expression "e^(ikr)" in the context of electromagnetic wave equations. Participants explore different methods of arriving at this expression, including references to the general solution of the wave equation and the use of four-vectors in relativistic approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about the origin of "e^(ikr)" and express confusion regarding its context and relevance.
  • One participant mentions the general solution of the wave equation, suggesting that it involves making an educated guess about the form of the solution.
  • Another participant points out that the electric field expression includes "E°e^(ikr)" and indicates that the author provides a specific value for r, leading to further questions about the calculation methods used.
  • There is a mention of a different calculation method involving "2pifn.x = wt - 2pifn.x," which some participants find perplexing.
  • A later reply introduces the concept of treating space and time as a four-vector, noting the importance of sign conventions in the inner product, which adds complexity to the discussion.
  • One participant expresses frustration and confusion, indicating a lack of clarity in the questions being asked.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple competing views regarding the interpretation and derivation of the expressions discussed. Confusion and differing methods of calculation contribute to the unresolved nature of the discussion.

Contextual Notes

There are limitations in the clarity of the questions posed, and some assumptions about the background knowledge of participants may not be met. The discussion also reflects varying approaches to the wave equation and its solutions, which may depend on different mathematical frameworks.

arslan786786
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how we get "e^(ikr)"...?
Plz ans me... Thanks
 
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arslan786786 said:
how we get "e^(ikr)"...?
Plz ans me... Thanks
Though it's e^(e(x-ct))
 
arslan786786 said:
how we get "e^(ikr)"...?
Though it's e^(e(x-ct))
There's no ##r## in the discussion above, so it's not clear what you're asking about when you write ##e^{(ikr)}##, nor does ##e^{e(x-ct)}## make sense in the context of this discussion.

Are you familiar with the general solution of the wave equation? It's a differential equation so we solve it by making an educated guess as to the general form of the solution (in this case, ##Ae^{i(\omega t-kx)}##), plugging it into our differential equation, and then solving for for the constants ##k## and ##\omega##. Do it right, and you'll get an equation describing a wave traveling at speed ##c##; post #6 by @RPinPA tells you how to interpret it.

(Once you've clarified your question, it may make sense to move it to a thread of its own)
 
sir please look at the electric field expression...
They are writing E°e^(ikr). The author puts r value...
I have searched a lot for it and I found its solution...
But i found that they calculate it with a very different method... They calculate 2pifn. x= wt-2pifn.x...
You can see in the image below...
So please guide me😕🙁
Screenshot_20210402-222812.png
 
Screenshot_20210402-222104.png
here is the screen shot sir...!
 
arslan786786 said:
sir please look at the electric field expression...
They are writing E°e^(ikr). The author puts r value...
I have searched a lot for it and I found its solution...
But i found that they calculate it with a very different method... They calculate 2pifn. x= wt-2pifn.x...
You can see in the image below...
So please guide me😕🙁View attachment 280809
Instead of treating space as a vector and time as a scalar, they are using the relativistic approach of a four-vector which combines the two into a single vector with 4 terms. Notice that the inner product is positive for the time term and negative for the space term. Some use the opposite sign convention for the inner product so one should be careful.
 
arslan786786 said:
View attachment 280810here is the screen shot sir...!
No idea what you are even asking.
 

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