Complex Representation of Moving EM Waves

In summary, the conversation discusses the complex representation of two wave functions, one moving in the negative x-axis and the other moving in the right axis. The equations for these wave functions are given and it is suggested that writing them in complex form allows for a simpler representation of both amplitude and phase. A resource is also provided for further understanding.
  • #1
rsaad
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Homework Statement



Moving in negative x-axis: E1 = E sin(wt + kx)
Moving in right axis: E2 = Esin(wt-kx-θ) moving to right

write complex representation


The Attempt at a Solution



E1= E Im(exp[i*(wt+kx)])
E2= E Im(exp[i*(wt-kx-θ)])

are these correct or do I have to take into account the -i^ for moving to left in E1?
 
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  • #2
As I understand it, the advantage of writing the wave function in complex form is that a single complex constant encapsulates both the amplitude and the phase. So you should get equations without a separate constant for phase. See e.g. http://farside.ph.utexas.edu/teaching/315/Waves/node72.html
 

What is the complex representation of moving electromagnetic waves?

The complex representation of moving electromagnetic waves is a mathematical representation of the electric and magnetic fields of a wave in terms of complex numbers. It is used to simplify calculations and analysis of electromagnetic waves in physics and engineering.

How is the complex representation of moving electromagnetic waves different from the traditional representation?

The traditional representation of electromagnetic waves uses real numbers to describe the electric and magnetic fields, while the complex representation uses complex numbers. This allows for a more concise and efficient way of representing and analyzing waves.

What are the benefits of using the complex representation of moving electromagnetic waves?

Using the complex representation allows for easier mathematical operations and simplifies the equations used to describe electromagnetic waves. It also allows for a better understanding of the properties and behavior of waves.

Can the complex representation be used for all types of electromagnetic waves?

Yes, the complex representation can be used for all types of electromagnetic waves, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Are there any disadvantages to using the complex representation of moving electromagnetic waves?

One potential disadvantage is that it may be more difficult for non-mathematicians to understand and work with complex numbers. Additionally, the complex representation may not be necessary for simple or basic calculations involving electromagnetic waves.

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