Jump conditions for Maxwell equations and their consequences

We derived the jump conditions for Faraday's induction law at the interface of two contacting bodies in both Eulerian and Lagrangian descriptions. An algorithm to implement the jump conditions in the potential formulation of Maxwell equation is presented. Calculations show that the use of the correct jump conditions leads to good agreement with experimental data, whereas the use of incorrect jump conditions can lead to severe inaccuracies in the computational results. Our derivation resolves the jump condition discrepancy found in the literature and is validated with experimental results.