EM Wave Energy: Proportional to Ampt Squared

In summary, the energy density of an EM wave is proportional to the amplitude squared because of the equation U = (E2 + B2)/2, where c = μ0 = ε0 = 1. The average value of E2 is proportional to Emax2, regardless of how fast E is varying, resulting in the average energy density not depending on ω. However, the electric field, which is also proportional to the acceleration of the charge, can vary with ω. This is because the key factor in determining Uavg is the average value, not the maximum value, of E. Therefore, Uavg is not dependent on ω, even though Emax may be.
  • #1
Hydr0matic
197
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 [Broken]

Hmmm... If U ∝ E2, E ∝ a and a ∝ ω, how can Uavg not be dependent on ω ?
 
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  • #2
I believe that the key word here is AVERAGE.
 
  • #3
Why ? If Emax depends on ω, then so should Uavg.
 
  • #4
Have I missunderstood something ? Will the amplitude of E increase when the oscillating charge accelerates faster ?
 

1. What is EM wave energy?

EM wave energy refers to the energy carried by electromagnetic waves, which are a type of energy that travels through space in the form of oscillating electric and magnetic fields.

2. How is EM wave energy related to amplitude squared?

The energy of an electromagnetic wave is directly proportional to the square of its amplitude. This means that as the amplitude increases, the energy also increases by a factor of the square of the amplitude.

3. Why is the relationship between EM wave energy and amplitude squared important?

Understanding the relationship between EM wave energy and amplitude squared is important because it helps us to understand how the energy of electromagnetic waves can be manipulated and controlled.

4. How does the amplitude of an EM wave affect its energy?

The amplitude of an EM wave is directly proportional to its energy. This means that increasing the amplitude of an EM wave will increase its energy, while decreasing the amplitude will decrease its energy.

5. Is the relationship between EM wave energy and amplitude squared always true?

Yes, the relationship between EM wave energy and amplitude squared is always true. This is because the energy of an EM wave is directly proportional to the square of its amplitude, regardless of the frequency or wavelength of the wave.

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