(adsbygoogle = window.adsbygoogle || []).push({}); "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" [Broken] 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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# Back of the envelope derivation of Larmor's equation

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