Approximate a plane E&M wave with this large sum....

In summary, the construction will approximate the electric and magnetic fields of a plane electromagnetic wave.
  • #1
Spinnor
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I would like to approximate a plane electromagnetic wave with a very large sum of the following.

Let an infinite line, say the z axis, have a electric polarization on that line and perpendicular to that line, say the x direction to be specific given by,

P(z,t) = pcos(kz-ωt). The polarization is a function of both space and time. Now let there be a uniform density of such lines in all space all parallel to one another, all in phase, and with them all polarized in the x direction. Will such a construction approximate the electric and magnetic fields of plane E&M wave?

Thanks!
 
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  • #2
Spinnor said:
I would like to approximate a plane electromagnetic wave with a very large sum of the following.

Let an infinite line, say the z axis, have a electric polarization on that line and perpendicular to that line, say the x direction to be specific given by,

P(z,t) = pcos(kz-ωt). The polarization is a function of both space and time. Now let there be a uniform density of such lines in all space all parallel to one another, all in phase, and with them all polarized in the x direction. Will such a construction approximate the electric and magnetic fields of plane E&M wave?

Thanks!
I just cannot understand the question. How can we have polarisation on that line and also perpendicular to it?
 
  • #3
tech99 said:
I just cannot understand the question. How can we have polarisation on that line and also perpendicular to it?

Just imagine at each point of the line a polarization vector that is also perpendicular to the line. Polarization is charge times a distance, just imagine the distance is very small, as small as you wish with charge increased so that distance times charge is a constant. Let the distance be of order the string length in string theory, that is pretty damn small.

Sorry for the confusion.
 

Related to Approximate a plane E&M wave with this large sum....

1. What is an E&M wave?

An E&M wave, also known as an electromagnetic wave, is a type of wave that is created by the oscillation of electric and magnetic fields. These waves are responsible for many natural phenomena, such as light, radio waves, and x-rays.

2. How can a plane E&M wave be approximated?

A plane E&M wave can be approximated by using a large sum of simpler waves, such as sine waves. This sum of simpler waves can be used to model more complex E&M waves with greater accuracy.

3. Why is it important to approximate E&M waves?

Approximating E&M waves is important because it allows us to better understand and predict the behavior of these waves in different situations. This is especially useful in fields such as telecommunications, where accurate wave modeling is crucial.

4. What factors affect the accuracy of the approximation?

The accuracy of the approximation depends on factors such as the number of simpler waves used in the sum, the amplitude and frequency of each wave, and the distance and direction of the wave from the observer. Additionally, any interference or distortion from external factors can also affect the accuracy of the approximation.

5. Are there any limitations to approximating E&M waves?

Yes, there are limitations to approximating E&M waves. As the complexity of the wave increases, it becomes more difficult to accurately approximate it using a large sum of simpler waves. Additionally, the approximation may not account for all factors that could affect the behavior of the wave in a real-world scenario.

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