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/content/aapt/journal/ajp/83/3/10.1119/1.4906577
1.
1. J. Franklin and D. J. Griffiths, “ The fields of a charged particle in hyperbolic motion,” Am. J. Phys. 82, 755763 (2014). All figure and equation numbers refer to this paper.
http://dx.doi.org/10.1119/1.4875195
2.
2.The connecting field comes from the infinitesimally brief moment when the motion transitions from uniform velocity to hyperbolic. In J. J. Thomson's classic model of a charge that starts or stops ( E. M. Purcell and D. J. Morin, Electricity and Magnetism, 3rd ed. ( Cambridge U.P., Cambridge, 2013), Sect. 5.7), the velocity is discontinuous, so the acceleration is a delta function. In our case, the acceleration is discontinuous, and the delta function is in the jerk. But the Liénard–Weichert field [Eq. (2)] does not explicitly involve the jerk, and it does not pick up a delta function. We thank D. Cross for this observation.
3.
3.For further details, see J. Franklin, “ Electric field of a point charge in truncated hyperbolic motion,” e-print arXiv:1411.0640v3.
4.
4.Cross has also shown how one can obtain the “extra” delta-function term directly from the Liénard–Weichert construction, without truncating the hyperbolic motion. See D. J. Cross, “ Completing the Liénard–Weichert potentials: The origin of the delta function for a charged particle in hyperbolic motion,” Am. J. Phys. (accepted); e-print arXiv:1409.1569.
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/83/3/10.1119/1.4906577
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2015-03-01
2016-12-04

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