EM Wave Energy: Proportional to Ampt Squared

AI Thread Summary
The discussion centers on the relationship between energy density in electromagnetic (EM) waves and the amplitude of the electric field. It is established that the energy density U of an EM wave is given by the equation U = (E² + B²)/2, where E is the electric field and B is the magnetic field. The average value of E² is proportional to the square of the maximum electric field (Emax²), indicating that the average energy density does not depend on the frequency (ω) of the wave. This is clarified by the distinction between average values and instantaneous values, emphasizing that while Emax may vary with ω, the average energy density remains constant. The discussion also touches on the relationship between electric field strength, charge acceleration, and how these factors influence the amplitude of the electric field, leading to questions about the dependency of average energy density on frequency.
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 ?
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'
So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
Back
Top