Question about energy in EM waves

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SUMMARY

The discussion centers on the relationship between the energy density of electromagnetic (EM) waves and radiation pressure. The instantaneous energy density is defined as u = ε₀E² [J/m³], while the average energy density is uavg = (1/2)ε₀E₀² [J/m³]. It is established that the average energy density is equivalent to the radiation pressure when fully absorbed, represented as Prad = / c [Pa]. The confusion arises from the units, but it is confirmed that 1 Pa is indeed equal to 1 J/m³, validating the equivalence of energy density and radiation pressure for EM waves.

PREREQUISITES
  • Understanding of electromagnetic wave properties
  • Familiarity with the concepts of energy density and radiation pressure
  • Knowledge of the constants ε₀ (permittivity of free space) and c (speed of light)
  • Basic grasp of unit conversions in physics
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  • Research the derivation of energy density in electromagnetic waves
  • Learn about the implications of radiation pressure in various applications
  • Study the relationship between energy density and momentum in EM waves
  • Explore advanced topics in electromagnetism, such as Maxwell's equations
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Students of physics, particularly those studying electromagnetism, as well as educators and professionals seeking clarity on the relationship between energy density and radiation pressure in electromagnetic waves.

mathplease
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The instantaneous energy density of a region of space of an EM wave is:

u = \epsilon0E2 [J/m^3]

hence the average energy density is:

uavg = (1/2)\epsilon0E02 [J/m^3]

uavg = <S> / c [J/m^3]

Is this equal to the wave's average http://en.wikipedia.org/wiki/Radiation_pressure" measured in [Pa] if the radiation is fully absorbed?

Prad= <S> / c [Pa]

My physics lecturer said these are not the same as one is measured in [J/m^3] and one is in [Pa], which seems clearly wrong to me but I'm worried I may have a misunderstanding in these concepts. Any confirmation or clarity is appreciated.
 
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mathplease said:
My physics lecturer said these are not the same as one is measured in [J/m^3] and one is in [Pa], which seems clearly wrong to me but I'm worried I may have a misunderstanding in these concepts. Any confirmation or clarity is appreciated.
I don't know if you are wrong or right, but the argument given doesn't work:
1 Pa = 1 J/m³ = 1 kg/(m s²)
So the units do work correctly.
 
Yes, for an electromagnetic wave the energy density is equal to the radiation pressure.
 

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