Determination of the boundary value problem of the electromagnetic field over a closed regular boundary

The main aim of this theoretical study is to verify the uniqueness of the solution of boundary value problem defined by specifying the tangential components of the electromagnetic field over the closed regular boundary of a limited region containing a linear dielectric material. So, we have evaluated the components of the electric and magnetic fields and found that both fields do not vanish in any subregion or region, and the uniqueness of the solution is proved in case of both fixed and continuously varying dielectric.