- #1
FranzDiCoccio
- 342
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"back of the envelope" derivation of Larmor's equation
Hi all,
I stumbled on a derivation of the Larmor's equation for the power radiated by an
accelerating charge that makes use of geometric arguments.
http://www.cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf" credits it to EM
Purcell.
The derivation seems nice, perhaps for recalling how things work without cumbersome
calculations. However, there is something I do not completely get.
The geometric argument shows that the electric field has a component perpendicular
to the radial direction. This is convincing enough. What I do not completely understand
is how they calculate the ratio of the radial and orthogonal component of the field.
The ratio they use applies to the "kink" in the field lines (this is clearer in the second
derivation). But how are the radial and azimuthal components
of the "kink" (i.e. a portion of field line) connected to the same components of the field
itself? Isn't the field amplitude related to the density of the field lines?
I sort of see that the field lines are denser when [tex]\theta = \pi/2[/tex], but doesn't that
affect both components equally (radial and azimuthal)?
Does any of you see a simple argument to relate the field amplitude in a certain direction
to the projection of the "kink" in that direction?
Thanks a lot for any insight
F
Hi all,
I stumbled on a derivation of the Larmor's equation for the power radiated by an
accelerating charge that makes use of geometric arguments.
http://www.cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf" credits it to EM
Purcell.
The derivation seems nice, perhaps for recalling how things work without cumbersome
calculations. However, there is something I do not completely get.
The geometric argument shows that the electric field has a component perpendicular
to the radial direction. This is convincing enough. What I do not completely understand
is how they calculate the ratio of the radial and orthogonal component of the field.
The ratio they use applies to the "kink" in the field lines (this is clearer in the second
derivation). But how are the radial and azimuthal components
of the "kink" (i.e. a portion of field line) connected to the same components of the field
itself? Isn't the field amplitude related to the density of the field lines?
I sort of see that the field lines are denser when [tex]\theta = \pi/2[/tex], but doesn't that
affect both components equally (radial and azimuthal)?
Does any of you see a simple argument to relate the field amplitude in a certain direction
to the projection of the "kink" in that direction?
Thanks a lot for any insight
F
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