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FireBones
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I was looking into propagation of EM waves, and it appears there is an overlooked nuance here. It is often said that EM-waves are self-propagating because a change in the E-field causes a magnetic field nearby, so a constantly changing E-field [i.e. a "vibrating" field] causes a constantly changing M-field.
All well and good, and if you look at the super-standard images showing EM-waves the mathematics works out fine [using the right-hand rule to show at each point the magnetic field you get is in the right direction and with the right size based on the changing E-fields, etc.]
Here is an example of what I mean. Using the right-hand rule for magnetic field generated by a changing electric field gives the correct answer [the field is moving out of the page with a small magnitude]
In the figure below, the gray areas represent regions contributing to a magnetic field at A that comes out of the page. That is, regions to its left where the electric field is decreasing or regions to its right where it is increasing. The other areas are regions that contribute to a magnetic field going into the page.
But it seems all of that breaks down at the front of the wave. At that point you end up sometimes getting results the opposite of what you would expect (essentially the line integrals used to determine size/direction of EM field are missing part of their loops because the EM perturbation has not reached points farther along.
If you imagine that point A is very near the front of the wave, and thus that there is no electric field disturbance far to the right, then the increasing electric field to its left will cause the magnetic field there to go the wrong way, as it is not balanced by an increasing electric field to its right.
Normally, the change in an electric field near a point determines the magnetic field due to the attenuation with distance [which is why the gray areas to the left do not overcome the significant white area closer to the point.]
Is the solution here that the front of an EM wave has modulated amplitude? So the change in the white area shown is relatively small compared to the change in the gray area farther to its left? Thus allowing that larger gray area, though it be farther away, to cause a net magnetic field coming out of the page [i.e., the direction it is supposed to be going?]
That is my assumption, but I was hoping for some verification.
Thanks.
All well and good, and if you look at the super-standard images showing EM-waves the mathematics works out fine [using the right-hand rule to show at each point the magnetic field you get is in the right direction and with the right size based on the changing E-fields, etc.]
Here is an example of what I mean. Using the right-hand rule for magnetic field generated by a changing electric field gives the correct answer [the field is moving out of the page with a small magnitude]
In the figure below, the gray areas represent regions contributing to a magnetic field at A that comes out of the page. That is, regions to its left where the electric field is decreasing or regions to its right where it is increasing. The other areas are regions that contribute to a magnetic field going into the page.
But it seems all of that breaks down at the front of the wave. At that point you end up sometimes getting results the opposite of what you would expect (essentially the line integrals used to determine size/direction of EM field are missing part of their loops because the EM perturbation has not reached points farther along.
If you imagine that point A is very near the front of the wave, and thus that there is no electric field disturbance far to the right, then the increasing electric field to its left will cause the magnetic field there to go the wrong way, as it is not balanced by an increasing electric field to its right.
Normally, the change in an electric field near a point determines the magnetic field due to the attenuation with distance [which is why the gray areas to the left do not overcome the significant white area closer to the point.]
Is the solution here that the front of an EM wave has modulated amplitude? So the change in the white area shown is relatively small compared to the change in the gray area farther to its left? Thus allowing that larger gray area, though it be farther away, to cause a net magnetic field coming out of the page [i.e., the direction it is supposed to be going?]
That is my assumption, but I was hoping for some verification.
Thanks.