Trying to understand electromagnetic waves

In summary: So the potential at a point changes as the field propagates (or slows down as it gets farther away), and that's what φ reflects.In summary, the potential at a point changes as the field propagates.
  • #1
Agustin.R
2
0
I'm having some trouble understanding visually the propagation of an electromagnetic wave. I'm self-studying electrodynamics so I've never had someone explain this properly to me.

I understand an electromagnetic wave is a propagating disturbance in an electromagnetic field. Originally, I thought this is a change in the radiating particle's field, so I was puzzled why wouldn't the wave fall off like r^2 like the electric field does. So I'm thinking that the electromagnetic wave is a separate, self-propagating electromagnetic field, distinct from the particle's field (or at least the field at the retarded time in which the particle radiated). Is this the meaning of "a changing electric field generating a magnetic field, and a changing magnetic field generating an electric one"?

Additionally, I don't understand what is the "Eo" value in the wave equation for a monochromatic plane wave. I know this is the amplitude, but I don't understand how I would calculate it.

Finally, most books I see have only a treatment of plane waves. Could anyone recommend me a book with a good treatment of spherical ones?

Thank you in advance for your help.
 
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  • #2
Agustin, This can lead to complicated math in a hurry, so I'll talk about about a simplified situation. Suppose you have two point charges located at z = +a and z = -a, and suppose the charges are equal and opposite and their magnitude varies sinusoidally: Q = ± Q0 eiωt. In between them there is a thin resistance-free wire that carries the current back and forth.

Let the field point be a distance r from the origin, and distances ra, rb from the charges. Look at the scalar potential, which depends only on the charges, not the current. It's like 1/r:

φ = Q0 [eiωt/ra - eiωt/rb]

But that's wrong: we ignored the effect of retardation. Changes in the field propagate outward at the speed of light, and φ reflects the value of each charge at the retarded time. So φ is really:

φ = Q0 [eiω(t-ra/c)/ra - eiω(t- rb/c)/rb]

Let ω = ck, and for utter simplicity take a field point somewhere on the z-axis, so that ra = r + a, rb = r - a.

φ = Q0 eikct -ikr[e-ika/(r+a) - e+ika/(r-a)]

Expand this, assuming the charges are close together: a << r and ka << 1. The leading terms are:

φ = Q0 eikct -ikr[-2ika/r - 2a/r2]

(I hope I got that right.) Anyway the point is, when k ≠ 0 (time-varying) the potential goes like 1/r, and when k=0 (static) the 1/r term is missing and the potential goes like 1/r2.
 

1. What is an electromagnetic wave?

An electromagnetic wave is a type of energy that consists of electric and magnetic fields oscillating at right angles to each other and traveling through space at the speed of light.

2. How are electromagnetic waves produced?

Electromagnetic waves are produced by the acceleration of charged particles. This can occur naturally, such as in lightning strikes, or artificially through electronic devices like radios and cell phones.

3. What are the different types of electromagnetic waves?

The electromagnetic spectrum includes a wide range of waves, from low frequency radio waves to high frequency gamma rays. This spectrum is divided into different categories, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays.

4. How do electromagnetic waves interact with matter?

Electromagnetic waves can interact with matter in a variety of ways. Some waves, like radio waves, can pass through matter with little resistance. Others, like x-rays, can be absorbed or scattered by matter. The specific interactions depend on the properties of the material and the frequency of the electromagnetic wave.

5. What are the practical applications of electromagnetic waves?

Electromagnetic waves have countless practical applications in our daily lives. They are used in communication technologies, such as radios, television, and cell phones. They are also used in medical imaging, like x-rays and MRI scans, and in industrial processes, like welding and heat treatments. Additionally, electromagnetic waves play a crucial role in understanding the universe through technologies like telescopes and satellites.

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