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Erratum: “The fields of a charged particle in hyperbolic motion” [Am. J. Phys. 82
, 755–763 (2014)]
1. J. Franklin and D. J. Griffiths, “ The fields of a charged particle in hyperbolic motion,” Am. J. Phys. 82, 755–763 (2014). All figure and equation numbers refer to this paper.
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.
For further details, see J. Franklin
, “ Electric field of a point charge in truncated hyperbolic motion
,” e-print arXiv:1411.0640v3
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
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