Impedance boundary conditions for transient scattering problems

The approximate boundary conditions for the tangential component of the electric field and normal component of the magnetic field on the surface of a homogeneous body of finite conductivity (conductor or lossy dielectric) are derived for transient incident electromagnetic field. Scale factors for basic variables are introduced in such a way, that a small parameter, proportional to the ratio of the penetration depth and body's characteristic size, appears in the dimensionless Maxwell's equations for the conducting region and then the perturbation method is used. The use of the boundary conditions together with space-time domain surface integral equations for electric and magnetic fields is proposed. A numerical example is included to illustrate the theory.