Interface conditions for the polarization vector. Given the interface conditions for the electric field intensity and the electric flux density in Table 4.3:
(a) Find the interface conditions required for the polarization vector at the interface between two dielectrics of permittivity ε1 and ε2. First, assume no free charges on the interface and then allow for existence of free charges on the interface.
(b) Determine the ratio of the normal and tangential components of the polarization vector at the interface between two perfect dielectrics with permittivity ε1 and ε2 in terms of the relative permittivity of the two perfect dielectrics. Assume there are no charges at the interfaces.
