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e2m2a
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This is not a homework question. Please do not delete it. I am 57 years old and trust me I am not in school. Doe the magnitude of the Poynting vector depend on the frequency of the wave hitting the surface?
e2m2a said:This is not a homework question. Please do not delete it. I am 57 years old and trust me I am not in school. Doe the magnitude of the Poynting vector depend on the frequency of the wave hitting the surface?
The Poynting vector is NOT the momentum density of the field.kcdodd said:Nope. The poynting vector simply gives you the momentum density of the field at some point.
clem said:The Poynting vector is NOT the momentum density of the field.
It is the intensity and represents the energy per unit time per unit area transmitted by the fields. It depends on the frequency only to the extent that E and B do. As usually used, the Poynting vector is averaged over time, much like the power in an AC circuit, so any frequency dependence averages out.
[tex]E=E_0 \sin(\omega t - \phi) [/tex]e2m2a said:How does E and B depend on the frequency?
In normal, linearly polarized plane waves E is proportional and perpendicular to B. [tex]\mathbf{B} = \frac{1}{c_0} \hat{\mathbf{k}} \times \mathbf{E}[/tex]I've looked all over and haven't seen anything that shows a proportional relationship, although it would seem that is the case.
For example, wouldn't a blue monochromatic light be transfering more energy per unit time than a red monochromatic light?
kcdodd said:I don't think that is what the op was asking. You're talking about dependence in the sense that something depends on position or time, only you have transformed it to Fourier space. I am pretty sure the op was talking about a fundamental dependence like energy = h*f. Fields have no fundamental dependence on space and time. Invariance of the field equations under these transformations is what leads to the conservation theorems.
Something must be changing if intensity increases with respect to the moving frame. Going back to the basic definition of intensity, we have energy density times velocity. Relative to the moving frame the intensity does increase with respect to the blue shifted light. Now of course the speed of light is still c in this frame, so something else must account for the increase in the energy density times velocity formula. There must be an increase in the energy density of the light wave with respect to the moving frame per unit of time. Blue shifted light photons in a given volume of space would give a greater energy density than red shifted light photons in the same given volume of space.kcdodd said:That's an interesting point. Looking at the lorentz transformation of the fields boosted along the x direction, where Ey and Bz are the field, and Ex, Ez, By, Bx = 0. (poynting vector points in x direction)
[tex]E'_y = \gamma (E_y - \beta B_z)[/tex]
[tex]B'_z = \gamma(B_z - \beta E_y)[/tex]
[tex]E'_y \times B'_z = \gamma^2 (E_y \times B_z - \beta E_y \times E_y - \beta B_z \times B_z +\beta^2 B_z \times E_y) = \gamma^2 (1 - \beta^2) E_y \times B_z = E_y \times B_z [/tex]
I don't see it changing here.
Does the magnitude of the Poynting vector depend on the frequency of the wave hitting the surface?
e2m2a said:... But I have also learned, according to Einstein's special theory, that the intensity of the light will be affected too. That is, the intensity of the blue-shifted light will increase and the intensity of the red-shifted light will decrease. Since the Poynting vector is an intensity entity, joules per second per meter squared, then the magnitude of the Poynting vector relative to this moving observer will be greater on the blue-shifted side and less on the red-shifted side. So, it appears that frequency and the Poynting vector(intensity) are linked, at least in this relativistic sense. Am I misunderstanding something here?
Yes, the Poynting Vector is frequency dependent. This means that its magnitude and direction can change with respect to the frequency of the electromagnetic wave.
The frequency of an electromagnetic wave affects the Poynting Vector by changing the magnitude and direction of the vector. As the frequency increases, the magnitude of the vector also increases. Additionally, the direction of the vector may also change.
The relationship between frequency and the Poynting Vector is directly proportional. This means that as the frequency increases, the magnitude of the Poynting Vector also increases.
Yes, the Poynting Vector can change in a vacuum. This is because the magnitude and direction of the vector are dependent on the properties of the medium through which the electromagnetic wave is traveling.
It is important to consider the frequency dependence of the Poynting Vector because it allows us to understand how the energy of an electromagnetic wave is distributed. This information is crucial in various applications, such as telecommunications and energy harvesting.