Feynman's Relativistic Electrodynamics Paradox

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A charged particle is located on the axis with its velocity pointing along the
axis. Another charged particle is also located on the
axis, but with its velocity pointing along the negative
axis. The net relativistic electric force on both particles is given by
, where
is the Coulomb constant,
is the factor
,
is the charge, and
is the position of the
particle. â¨The relativistic magnetic force of particle 2 on 1 is
. The magnetic force of particle 1 on 2 is zero. The momentum of the electromagnetic field is given by the time derivative of the vector potential
in the Coulomb gauge,
. The sum of all three terms is zero and shows momentum conservation. The contour lines show the relativistic Liénard–Wiechert potential for each charge.
Contributed by: Adam Caprez and Herman Batelaan (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
For more information see A. Caprez and H. Batelaan, "Feynman's Relativistic Electrodynamics Paradox and the Aharonov-Bohm Effect," Foundations of Physics 39(3), 2009 pp. 295–306.
Permanent Citation
"Feynman's Relativistic Electrodynamics Paradox"
http://demonstrations.wolfram.com/FeynmansRelativisticElectrodynamicsParadox/
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Published: March 7 2011