Transcription of Dielectric Boundary Conditions - ITTC
1 11/4/2004 Dielectric Boundary 1/4 Jim Stiles The Univ. of Kansas Dept. of EECS Dielectric Boundary Conditions Consider the interface between two dissimilar Dielectric regions: Say that an electric field is present in both regions, thus producing also an electric flux density (()()rr =DE). Q: How are the fields in Dielectric region 1 ( , ()()11r, r D) related to the fields in region 2 ( , ()()22r, r D)? A: They must satisfy the Dielectric Boundary Conditions !
2 ()()11r, r D()()22r, r D1 2 11/4/2004 Dielectric Boundary 2/4 Jim Stiles The Univ. of Kansas Dept. of EECS First, let s write the fields at the Dielectric interface in terms of their normal (()rnE) and tangential (()rtE) vector components: Our first Boundary condition states that the tangential component of the electric field is continuous across a Boundary . In other words: ()()12rrtbtb=EE where rbdenotes any point on the Boundary ( , Dielectric interface). ()()()11 1rrrtn=+ ()1rn 1 2 na()1rt ()2rt ()2rn ()()()22 2rrrtn=+ 11/4/2004 Dielectric Boundary 3/4 Jim Stiles The Univ.
3 Of Kansas Dept. of EECS The tangential component of the electric field at one side of the Dielectric Boundary is equal to the tangential component at the other side ! We can likewise consider the electric flux densities on the Dielectric interface in terms of their normal and tangential components: The second Dielectric Boundary condition states that the normal vector component of the electric flux density is continuous across the Dielectric Boundary . In other words: ()()12rrnbnb=DD where rbdenotes any point on the Dielectric Boundary ( , Dielectric interface).
4 ()()111rr =D ()1rnD1 2 na()1rtD()2rtD()2rnD()()222rr=D 11/4/2004 Dielectric Boundary 4/4 Jim Stiles The Univ. of Kansas Dept. of EECS Since ()()rr=D , these Boundary Conditions can likewise be expressed as: ()()()()121212rrrrtbtbtbtb==EEDD and as: ()()()()121122rrrrnbnbnbnb==DDEE MAKE SURE YOU UNDERSTAND THIS: These Boundary Conditions describe the relationships of the vector fields at the Dielectric interface only ( , at points brr=)!!!! They say nothing about the value of the fields at points above or below the interface.
5
