Three dimensional electromagnetic field due to electric discharge by an analytical approach

The analytical expression of the time behaviour of the current density due to an electric discharge on a three dimensional conducting slab has been obtained by means of an analytical method. The electric discharge is modeled by a current pulse injected in the slab. The current injection point can be arbitrarily positioned on the surface of the slab. The diffusion equation was solved in the s domain using the technique of the separation of variables. The time behaviour of the current density was determined applying the inverse Laplace transform to the solution. The analytical results were compared with results obtained with two numerical methods, the first based on an equivalent network formulation and the second based on a Finite Difference Time Domain method. The electromagnetic field in space has been simply determined from the knowledge of the current density distribution