Acta Polytechnica Hungarica Vol. 17, No. 1, 2020 – 175 – A Repulsive Interaction in Classical Electrodynamics Katalin Gambár 1 , Mario C. Rocca 2 , Ferenc Márkus 3 1 Institute of Microelectronics and Technology, Kálmán Kandó Faculty of Electrical Engineering, Óbuda University, Tavaszmező u. 17, H-1084 Budapest, Hungary 2 Departamento de Física, Faculdad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina 3 Deparment of Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1521 Budapest, Hungary gambar.katalin@kvk.uni-obuda.hu, rocca@fisica.unlp.edu.ar, markus@phy.bme.hu Abstract: Herein, we introduce an additional term into the induction equation (one of the Maxwell’s equation). The related Lagrangian formalism applying the scalar and vector potentials is fitted to this modified Maxwell’s equations. In the framework of Hamiltons’s principle we are able to deduce Klein-Gordon equations with negative “mass term” for the field variables electric field E and magnetic induction B. We can conclude from the mathematical structure of the equations that a repulsive interaction appears. The Wheeler propagator can be calculated for the present case by which the time evolution of the field can be discussed. In spite of the situation that these equations have tachyon solutions, the results are in line with the causality principle. As a consequence of the theory, a spontaneous charge disjunction process may rise in the field. Keywords: Maxwell’s equations; Klein-Gordon equation with negative “mass term”; Lagrangian, Wheeler propagator; charge distribution 1 Introduction Mechanical [1, 2], thermodynamic [2-4] and further field theoretical examples [5- 7] for the Klein-Gordon equation with negative “mass term” involve the same dynamical phase transition that operates between the diffusive and the wave type dynamics. Studying the existence of these kinds of phenomena we may assume that the occurrence of these are more general and not restricted exclusively to a certain part of physics.