3. the Tangential Component of e As we know in the static case. the electric field is curless VXE=0, i.e. along any closed path c the integral IcE.dI=0 Taking a closed path around the boundary as shown in Fig 7-2, we have E11-Et2L=0,→E1=Et2
L Figure 7-2 Closed path of integration crossing the interface between two media I and 2. Whatever be the surface charge density a, the tangential components of E on either side of the interface are equal: En= en
4. Bending Of Lines of e From the boundary conditions it follows that the vectors D and e change directions at the boundary between two media.(SeeF「g73) Figure 7-3 Lines of D or of E crossing the interface between two media I and 2 The lines change direction in such a way that e, i tan 02=6, tan 0
For an interface with the free charge density of =0 from(Dnl -Dm2) - Of we have Di cos 01- D2 cos 82=0 or r1e0E1 cos 61= Er2E0 E2 cos 02 From the tangential component Et1= Et2, we have E1 sin 01- E2 sin B2 Combining these two equations yields tan T tan e2 Er2 The medium with the larger relative permittivity cr has a larger angle 0 from the normal