A
selection of references for the two-capacitor problem (one of which has already been given in this very thread)
The two-capacitor problem with radiationTimothy B. Boykin, Dennis Hite, and Nagendra Singh
Department of Electrical and Computer Engineering,
The University of Alabama in Huntsville, Huntsville, Alabama 35899
~Received 12 June 2001; accepted 8 November 2001; Published Online: 11 March 2002
American Association of Physics Teachers. @DOI: 10.1119/1.1435344
available upon request to the author from this ResearchGate page:
https://www.researchgate.net/publication/243492397_The_two-capacitor_problem_with_radiationCapacitors can radiate: Some consequences of the two-capacitor problem with radiation14 May 2003
T.C. CHOY
arXiv:physics/0305062v1 [physics.class-ph]
https://www.researchgate.net/publication/2168891_Capacitors_can_radiate_-_some_consequences_of_the_two-capacitor_problemwith_radiationfreely available at ResearchGate (direct link)
https://www.researchgate.net/profile/Tuck-Choy/publication/2168891_Capacitors_can_radiate_-_some_consequences_of_the_two-capacitor_problemwith_radiation/links/5935528daca272fc5556a317/Capacitors-can-radiate-some-consequences-of-the-two-capacitor-problem-with-radiation.pdfRadiative effects and the missing energy paradox in the two capacitor problemGilberto A Urzua, Omar Jimenez, Fernando Maass and Alvaro Restuccia
Departamento de Fisica, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile
E-mail: gilberto.urzua@uantof.cl, omar.jimenez@uantof.cl, fernando.maass@uantof.cl, alvaro.restuccia@uantof.cl
Journal of Physics: Conference Series 720 (2016) 012054
doi:10.1088/1742-6596/720/1/012054
https://www.researchgate.net/publication/303980311_Radiative_effects_and_the_missing_energy_paradox_in_the_ideal_two_capacitors_problemfreely available at ResearchGate (direct link)
https://www.researchgate.net/publication/303980311_Radiative_effects_and_the_missing_energy_paradox_in_the_ideal_two_capacitors_problem/fulltext/57a4bae308ae455e8539f85d/Radiative-effects-and-the-missing-energy-paradox-in-the-ideal-two-capacitors-problem.pdfThe two-capacitor problem revisited: a mechanical harmonic oscillator model approachKeeyung Lee
Department of Physics, Inha University, Incheon, 402-751, Korea
Received 17 July 2008, in final form 4 September 2008; Published 6 November 2008
EUROPEAN JOURNAL OF PHYSICS
Eur. J. Phys. 30 (2009) 69–74 doi:10.1088/0143-0807/30/1/007
Online at stacks.iop.org/EJP/30/69
Preprint available from ArXiv:
https://arxiv.org/abs/1210.4155Entropic Considerations of the Two-Capacitor ProblemJanuary 19, 2012
V.O.M. Lara, A. P. Lima, and A. Costa
Instituto de Fısica - Universidade Federal Fluminense
https://www.researchgate.net/publication/51990322_Entropic_considerations_on_the_Two-Capacitor_Problemfreely available at ResearchGate (direct link)
https://www.researchgate.net/profile/Ap-Lima/publication/51990322_Entropic_considerations_on_the_Two-Capacitor_Problem/links/55e9aa6208ae21d099c302fb/Entropic-considerations-on-the-Two-Capacitor-Problem.pdfThe Paradox of Two Charged Capacitors -- A New PerspectiveAugust 2013
Authors: Ashok K. Singal
Indian Space Research Organization arXiv
https://www.researchgate.net/publication/256762725_The_Paradox_of_Two_Charged_Capacitors_--_A_New_Perspective(direct link)
https://www.researchgate.net/profile/Ashok-Singal/publication/256762725_The_Paradox_of_Two_Charged_Capacitors_--_A_New_Perspective/links/559e349008ae76bed0bb6d46/The-Paradox-of-Two-Charged-Capacitors--A-New-Perspective.pdfThe idea I have come to so far:
You start with energy E, you end up with energy E/2 split between the two caps and E/2 lost in some way (doesn't actually matter which one and in which measure). Charge is conserved, voltage is the same.
The transformation is
irreversible, therefore some energy MUST be lost and entropy must increase.
Turns out that energy it can be lost in different ways, depending on the actual circuit: if there is appreciable resistance (a handful of microohms might suffice), it goes basically all into heat. If there is nearly no resistance or exactly zero resistance it goes into radiation (even without inductance in the loop) either by magnetic dipole or by electric dipole. If there is appreciable inductance it can go back and forth rapidly enough to lose energy by radiation of the LC oscillator (but it's usually the other ways that predominate).