- #1
arslan786786
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how we get "e^(ikr)"...?
Plz ans me... Thanks
Plz ans me... Thanks
Electromagnetic wave equation - phase and amplitude
- Thread starter arslan786786
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In summary, the electromagnetic wave equation is a mathematical representation of the propagation of electromagnetic waves through space. Phase is an important factor in the equation, determining the position of a wave in its cycle and allowing for the calculation of interference and superposition. The amplitude of an electromagnetic wave affects its strength and intensity. The equation is used in many practical applications, including wireless communication and understanding light and other forms of radiation. It can be applied to all types of electromagnetic radiation, aiding in the understanding of their properties and behavior.
- #2
arslan786786
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Though it's e^(e(x-ct))arslan786786 said:
- #3
Nugatory
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arslan786786 said:
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)
- #4
arslan786786
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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
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
- #5
arslan786786
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- 0
- #6
Frabjous
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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: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
- #7
Frabjous
Gold Member
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- 2,238
No idea what you are even asking.arslan786786 said:
FAQ: Electromagnetic wave equation - phase and amplitude
What is the electromagnetic wave equation?
The electromagnetic wave equation is a mathematical equation that describes the behavior of electromagnetic waves, which are a combination of electric and magnetic fields that propagate through space.
What is the significance of phase in the electromagnetic wave equation?
Phase refers to the position of a point on an electromagnetic wave at a given time. It is important because it determines the relative position of the peaks and troughs of the wave, which affects its amplitude and overall behavior.
How is amplitude related to the electromagnetic wave equation?
Amplitude is a measure of the strength or intensity of an electromagnetic wave. It is directly related to the energy carried by the wave and is determined by the electric and magnetic field strengths.
Can the phase and amplitude of an electromagnetic wave be changed?
Yes, the phase and amplitude of an electromagnetic wave can be changed through various means such as reflection, refraction, and diffraction. These changes can alter the behavior of the wave and its interactions with matter.
What are some real-life applications of the electromagnetic wave equation?
The electromagnetic wave equation is used in a wide range of fields, including telecommunications, radar and sonar systems, medical imaging, and satellite communication. It is also crucial in understanding the behavior of light and other electromagnetic radiation in various mediums.