BOUNDARY CONDITION FOR PERFECT DIELECTRICS




Consider the interface or the boundary between two dielectrics with different properties, L H  }1    }o}r1  DQG }2    }o}r2  are the permittivities of the two media 1 and 2. Assume that there are no free charges at the interface between the two media. If we construct a pillbox with infinitesimally small thickness and area.

if D->1  and D->2 are the electric flux densities or the displacement densities in the media 1and 2 respectively, then since there are no charges enclosed, it follows from Gauss’s law that  the  surface  integral of D  over  the  pill box surface  is zero.  Thus,  D->1.n1^ûV    D->2 .n^2ûV    ZKHUH ûs is the pillbox surface (top and bottom) and n^1  and n^2  are the unit outward normals respectively. Thus, (D->1  - D->2).n^1  =0. Since n^1  is the unit normal to the  interface,  D->1  -  D->2  =  0,  where  D->1  and  D->2  are  the  normal  components  of  the electric  flux densities  in the respective media. Thus D->1  = D->2.  The normal components of  displacement  densities  are  equal  at  the  boundary  between  two  dielectric  media.  In other  words,  the  normal  component  of  the  electric  flux  density  across  the  charge  free interface  between  the  two  media  is  continuous,  meaning  that  the  number  of  lines  of displacement flux entering one face is the same as the number leaving the other face.






The above relation is useful in evaluation of the flux density and hence field intensity- components in one medium due to those in the adjacent medium.

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