Question about energy in EM waves

In summary, the instantaneous energy density of an electromagnetic wave in a region of space is u = \epsilon0E2 [J/m^3]. The average energy density is uavg = (1/2)\epsilon0E02 [J/m^3], which is also equal to <S> / c [J/m^3]. This is equivalent to the wave's average radiation pressure, Prad= <S> / c [Pa], if the radiation is fully absorbed. Despite what the physics lecturer claimed, the units for energy density and pressure do match up correctly.
  • #1
mathplease
26
0
The instantaneous energy density of a region of space of an EM wave is:

u = [tex]\epsilon[/tex]0E2 [J/m^3]

hence the average energy density is:

uavg = (1/2)[tex]\epsilon[/tex]0E02 [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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  • #2
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.
 
  • #3
Yes, for an electromagnetic wave the energy density is equal to the radiation pressure.
 

FAQ: Question about energy in EM waves

What is the relationship between energy and frequency in EM waves?

The energy of an EM wave is directly proportional to its frequency. This means that as the frequency of the wave increases, so does its energy. This relationship is described by the formula E = hf, where E is energy, h is Planck's constant, and f is frequency.

Can EM waves transfer energy without a medium?

Yes, EM waves can transfer energy without a medium. This is because they are composed of oscillating electric and magnetic fields that can propagate through a vacuum. This is why we are able to receive radio signals and see objects illuminated by sunlight, even though there is no physical medium for the waves to travel through.

How does the energy of EM waves compare to other types of waves?

The energy of EM waves is higher than that of sound waves and lower than that of gamma rays. This is because the energy of a wave is directly related to its frequency, and EM waves have a higher frequency than sound waves but a lower frequency than gamma rays.

Can the energy of EM waves be harnessed for practical purposes?

Yes, the energy of EM waves can be harnessed for various practical purposes. For example, we use EM waves for communication (radio waves), cooking (microwaves), and imaging (x-rays). Additionally, solar panels are able to convert the energy of sunlight (which is composed of EM waves) into electricity.

How does the energy of an EM wave change as it travels through different materials?

The energy of an EM wave remains constant as it travels through different materials. However, the speed and wavelength of the wave may change depending on the material it is passing through. This is due to the wave's interaction with the atoms and molecules in the material, which can affect its speed and wavelength but not its energy.

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