EM Wave Energy: Proportional to Ampt Squared

Click For Summary

Discussion Overview

The discussion revolves around the relationship between the energy density of electromagnetic (EM) waves and their amplitude, specifically addressing why the energy density is proportional to the amplitude squared. Participants explore the implications of this relationship in the context of varying frequencies and charge acceleration.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that the energy density U of an EM wave is given by U = (E² + B²)/2, suggesting that the average value of E² is proportional to Emax², independent of the frequency ω.
  • Another participant questions how the average energy density can be independent of ω if Emax is dependent on ω, indicating a potential contradiction in the reasoning presented.
  • A further participant expresses confusion about whether the amplitude of the electric field E increases with faster acceleration of the oscillating charge, seeking clarification on this point.
  • One participant emphasizes the importance of the term "AVERAGE" in the context of energy density.

Areas of Agreement / Disagreement

Participants appear to disagree on the implications of the relationship between amplitude and energy density, particularly regarding the influence of frequency on average energy density. The discussion remains unresolved with multiple competing views presented.

Contextual Notes

There are unresolved questions regarding the dependence of energy density on frequency and the relationship between charge acceleration and electric field amplitude. Participants have not reached a consensus on these points.

Hydr0matic
Messages
196
Reaction score
1
The reason the energy density of an EM wave is proportional only to the amplitude squared is because electromagnetic energy density U is:

U = (E2 + B2)/2

in units where c = μ0 = ε0 = 1

The average value of E2 is proportional to Emax2, it doesn't matter how fast E is varying, so the average energy density doesn't depend on ω.

Hurkyl

The electric field is also proportional to the acceleration of the charge. The larger the acceleration, the larger is the field.
-> http://electron9.phys.utk.edu/optics421/modules/m1/production.htm

Hmmm... If U ∝ E2, E ∝ a and a ∝ ω, how can Uavg not be dependent on ω ?
 
Last edited by a moderator:
Physics news on Phys.org
I believe that the key word here is AVERAGE.
 
Why ? If Emax depends on ω, then so should Uavg.
 
Have I missunderstood something ? Will the amplitude of E increase when the oscillating charge accelerates faster ?
 

Similar threads

  • · Replies 21 ·
Replies
21
Views
4K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 39 ·
2
Replies
39
Views
6K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K