High frequency electrical oscillations in cavities
If the interior of a conducting cavity (such as a capacitor or a coaxial cable) is supplied with a very high-frequency electric signal, the information between the walls propagates with an appreciable delay, due to the finiteness of the speed of light. The configuration is typical of cavities having size larger than the wavelength of the injected signal. Such a non rare situation, in practice, may cause a break down of the performances of the device. We show that the classical Coulomb's law and Maxwell's equations do not correctly predict this behavior. Therefore, we provide an extension of the modeling equations that allows for a more reliable determination of the electromagnetic field during the evolution process. The main issue is that, even in vacuum (no dielectric inside the device), the fast variation of the signal produces sinks and sources in the electric field, giving rise to zones where the divergence is not zero. These regions are well balanced, so that their average in the domain is zero. However, this behavior escapes the usual treatment with classical electromagnetism.
 M. Born and E. Wolf. Principles of Optics. Pergamon Press, 1987.
 W. Cai. Computational Methods for Electromagnetic Phenomena: electrostatics in solvation, scattering, and electron transport. Cambridge University Press, 2013.
 D.K. Cheng. Fundamentals of Engineering Electromagnetics. III Edition. Addison-Wesley, 1993.
 3d electromagnetic simulation software. Available from Internet: https://www.cst.com/.
 W. Engelhardt. On the solvability of Maxwell's equations. Annales de la Fon-dation Louis de Broglie, 37(1):3-14, 2012. arXiv:1209.3260
 R.P. Feynman, R.B. Leighton and M. Sands. The Feynman Lectures on Physics.Addison-Wesley, 1963.
 D. Funaro. Electromagnetism and the Structure of Matter. World Scientific, Singapore, 2008.
 D. Funaro. From Photons to Atoms. The Electromagnetic Nature of Matter. arXiv: 1206.3110v1, 2012.
 D. Funaro. On the near-field of an antenna and the development of new devices. arXiv: 1203.1229v1, 2012.
 D. Funaro. Charging capacitors according to Maxwell's equations: impossible. Annales de la Fondation Louis de Broglie, 39:75-93, 2014. arXiv:1412.6005v1
 D. Funaro and E. Kashdan. Simulation of electromagnetic scattering with stationary or accelerating targets. International Journal of Modern Physics C, 26(7):1-16, 2015. https://doi.org/10.1142/S0129183115500758.
 D.J. Griffths. Introduction to Electrodynamics. IV Edition. Cambridge University Press, UK, 2017.
 T. Hart and P. Birke. The Poynting Vector Antenna. BookBaby, 2016.
 U.S. Inan and R.A. Marshall. Numerical Electromagnetics: The FDTD Method. Cambridge University Press, 2011.
 J.D. Jackson. Classical Electrodynamics. II Edition. John Wiley and Sons, 1975.
 A.L. Kholmetskii, O. Missevitch and R. Smirnov-Rueda. Measurement of propagation velocity of bound electromagnetic fields in near zone. Journal of Applied Physics, 102(1):013529, 2007. https://doi.org/10.1063/1.2749415.
 A.L. Kholmetskii, O. Missevitch, R. Smirnov-Rueda and T. Yarman. Propagation of electromagnetic fields in near and far zones: actualized approach with non-zero trace electro-magnetic energy-momentum tensor. Progress in Electromagnetics Research M, 22:57-62, 2012. https://doi.org/10.2528/PIERM1110140.
 O.V. Missevitch, A.L. Kholmetskii and R. Smirnov-Rueda. Anomalously small retardation of bound (force) electromagnetic fields in antenna near zone. EPL (Europhysics Letters), 93(6):64004, 2011. https://doi.org/10.1209/0295-5075/93/64004.
 P. Monk. Finite Element Methods for Maxwell's Equations. Clarendon Press, 2003. https://doi.org/10.1093/acprof:oso/9780198508885.001.0001.
 T. Rylander, P. Ingelstrom and A. Bondeson. Computational Electromagnetics. II Edition. Springer, 2013. https://doi.org/10.1007/978-1-4614-5351-2.