A New Proof on Boundary Conditions in Electromagnetic Theory
Although electromagnetic waves have been the subject of intense study by many researchers for many years,there still exist elementary yet fundamental aspects of the theory that have not been carried out.It is well known that,for time varying fields with a source free boundary,satisfying the continuity of the tangential electric and magnetic fields across the boundary surface of two different material media automatically implies the continuity of the normal magnetic induction vector and electric displacement vector across that boundary surface.However,the converse is not true.A proof on this statement has not been found in the literature.Here,we shall provide this proof.In addition,it will be shown that unlike the case for the time-varying fields,for the static field case,satisfying the boundary conditions on the tangential electric and/or magnetic fields does not imply the satisfaction of the boundary conditions on the normal electric displacement and/or magnetic induction fields.Boundary conditions are the cornerstones in electromagnetics 1-6.Although it is well known that for time-varying electromagnetic fields on a source free boundary,satisfying the continuity of electric(E)and magnetic(H)fields at the interface implies that the continuity conditions of the normal components of the magnetic induction vector(B)and the electric displacement vector(D)are satisfied,the converse is not true.In other words,for time varying electromagnetic fields,the satisfaction of the continuity conditions for the tangential E and H fields at a dielectric interface is a necessary and sufficient requirement,while the satisfaction of the continuity conditions for the normal B and D at that interface is only a necessary but not sufficient requirement.On the other hand,for time-independent(static)electric or magnetic fields,satisfying the continuity conditions on tangential E does not imply the satisfaction of the continuity of the normal component of B at the dielectric interface,and satisfying the continuity on tangential H does not imply the satisfaction of the continuity of the normal component of D at the interface.It is surprising to learn that the proof is not commonly known.The first proof,given by Yeh appeared in 1993 7,8 A different version is given here.
Cavour Yeh Fred Shimabukuro
California Advanced Studies,2432 Nalin Dr.,Los Angeles,CA 90077,USA
国际会议
Progress in Electromagnetics Research Symposium 2013(2013年电磁学研究新进展学术研讨会)
台北
英文
783-786
2013-03-01（万方平台首次上网日期，不代表论文的发表时间）