Electromagnetic wave equation - phase and amplitude

AI Thread Summary
The discussion centers on the expression "e^(ikr)" in the context of electromagnetic wave equations. Participants clarify that "e^(ikr)" is derived from the general solution of the wave equation, typically expressed as "Ae^(i(ωt-kx))". There is confusion regarding the use of "e^(e(x-ct))" and the role of the variable "r". The conversation also touches on different methods of calculating wave equations, including a relativistic approach using four-vectors. Overall, the thread highlights the complexities of wave equations and the need for clarity in mathematical expressions.
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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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