Radiation Pulse from an Accelerated Point Charge

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J. J. Thomson first suggested a pictorial representation of how an instantaneously accelerated point charge can produce a pulse of electromagnetic radiation. An electron, with charge , moving at a constant speed , even when a significant fraction of the speed of light , produces an electric field of magnitude , (add factor if you cannot live without SI units), where represents the projected position of the source charge at time , assuming that it continues to move at constant speed from its position at the retarded time . This is derived most lucidly in the Feynman Lectures [1]. Thus a uniformly moving point source emits a spherical longitudinal electric field, although its magnitude does vary with direction. This is represented in the graphic by a series of 12 uniformly spaced radial spokes.


The electron is assumed to move initially at a speed until time , when it reaches the red dot at the center of the figure. The charge is then, in concept, instantaneously accelerated to speed . For , the charge emits a longitudinal electric field characteristic of the speed . On a sphere of radius , shown in red (a ring of fire?), the field catches up with the field, which still behaves as if the electron were moving at its original speed. Since electric-field lines must be continuous in charge-free space, the two sets of field lines connect with transverse segments along the ring of fire, with an angular intensity proportional to . Transverse magnetic field lines , perpendicular to the lines (not shown on the graphic) are also created by the moving charge. The lengthening of the segments by a factor implies the long-range radial dependence of the radiation fields as , rather than , as for electrostatic fields.

Thus, it has been shown that pulses of electromagnetic radiation consist of transverse electric and magnetic fields moving radially outward with the speed of light from the point of instantaneous charge acceleration.


Contributed by: S. M. Blinder (May 2011)
Open content licensed under CC BY-NC-SA




[1] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II, Reading, MA: Addison–Wesley, 1964, pp. 26.1–26.4.

[2] E. M. Purcell, Electricity and Magnetism: Berkeley Physics Course, Vol. 2, New York: McGraw-Hill, 1984, pp. 331–334.

[3] D. V. Schroeder, "Purcell Simplified or Electricity, Magnetism, and Relativity." (January 1999) http://physics.weber.edu/schroeder/mrr/MRRtalk.html.

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