- #1
Zorba
- 77
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So suppose we have two dielectrics in contact and we want to know how [tex]\mathbf{D}[/tex] varies across them, then we can use the fact that since [tex]\nabla \cdot \mathbf{D} = \rho_f[/tex] and we have no "free" charges at the boundary then [tex]\mathbf{D}[/tex] is continuous across it.
So my question is, in Grant & Philips they seem to suggest that only the components of [tex]\mathbf{D}_{1,2}[/tex] that are perpendicular to the surface of contact of the dielectrics, are equal. Is it the case that the components parallel are not also equal? And if so why, because [tex]\nabla \cdot \mathbf{D} = \rho_f[/tex] seems to imply that they should be equal?
So my question is, in Grant & Philips they seem to suggest that only the components of [tex]\mathbf{D}_{1,2}[/tex] that are perpendicular to the surface of contact of the dielectrics, are equal. Is it the case that the components parallel are not also equal? And if so why, because [tex]\nabla \cdot \mathbf{D} = \rho_f[/tex] seems to imply that they should be equal?