《Electromagnetism, principles and application》教学课件（PPT讲稿）Chapter 7 Dielectrics：II

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 CE. dI Taking a closed path around the boundary as shown in Fig 7-2, we have Et1L-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 b on either side of the interface are equal: E =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. (See Fig 7-3) 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 0,=6: tan O

For an interface with the free charge density rom(DnI -Dn2)=af we have D1 cos 8 COS 02=0. Erico el cos 1= Er2eo e2 cos 82 From the tangential component Et1= Et2, we have 1 sIn 01=Bo sin 02 Combining these two equations yields tan tan The medium with the larger relative permittivity Er has a larger angle 0 from the normal