Physical meaning of parts of electromagnetic wave

In summary, the equations E = E_0exp i(k dot r - wt) and E = cos(k dot r - wt) represent a plane wave that occupies all of space. For a localized beam along a line, E_0 must be a function of distance from the line. The position r can be any position in space for the wave.
  • #1
littlepapa87
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in

E = E_0exp i(k dot r - wt) or E = cos(k dot r - wt)

what does k dot r physically represent? Can r be any position in space or must it lie on the wave?

(I physically understand what a dot product is)
 
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  • #2
That's a plane wave, it occupies all of space.

If you want a beam that is localized along a line, E_0 has to be a function of distance from the line.
 
  • #3
littlepapa87 said:
Can r be any position in space

Yes.

or must it lie on the wave?

A 3-dimensional plane wave fills space. It doesn't lie "along" a line or other single path. See the diagram and associated instructions in the following post for a more realistic picture of a plane electromagnetic wave than you see in many textbooks.

https://www.physicsforums.com/showpost.php?p=533190&postcount=6
 

What is an electromagnetic wave?

An electromagnetic wave is a type of energy that travels through space in the form of electric and magnetic fields. These waves are created by the movement of electrically charged particles, and they can travel through vacuum as well as through various mediums such as air or water.

What are the different parts of an electromagnetic wave?

An electromagnetic wave consists of two perpendicular components - an electric field and a magnetic field. The electric field is responsible for the movement of charged particles, while the magnetic field is perpendicular to the electric field and helps to maintain its oscillation.

What is the wavelength of an electromagnetic wave?

The wavelength of an electromagnetic wave is the distance between two consecutive peaks or troughs of the wave. It is usually measured in meters and can range from very small values (such as gamma rays) to very large values (such as radio waves).

What is the frequency of an electromagnetic wave?

The frequency of an electromagnetic wave is the number of oscillations per second of the electric and magnetic fields. It is measured in hertz (Hz) and is inversely proportional to the wavelength. This means that longer wavelengths have lower frequencies and vice versa.

What is the relationship between the energy and frequency of an electromagnetic wave?

The energy of an electromagnetic wave is directly proportional to its frequency. This means that waves with higher frequencies (such as x-rays and gamma rays) have more energy than waves with lower frequencies (such as radio waves and microwaves). This relationship is described by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency.

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