98 



BELL SYSTEM TECHNICAL JOURNAL 



rectangle A'B'B"A" with two of its sides parallel to the sheet (Fig. 2). 

 We assume that the current flows toward the reader and that A' A" 

 and B'B" are vanishingly small. Since the M.M.F. around this 

 rectangle is equal to the electric current passing through it and since 

 this M.M.F. is merely the difl"erence between the M.M.F.'s along the 

 sides A'B' and A"B'\ we obtain 



Ht' - ///' = Ji 



(13) 



by simply calculating these quantities per unit length of the rectangle. 

 The tangential components of the magnetic intensity are regarded as 



Fig. 2 — A cross-section of a current sheet perpendicular to the lines of flow. The 

 positive direction of the current is toward the reader. 



positive when directed from A to B. Thus the tangential component 

 of the magnetic intensity is discontinuous across an electric current 

 sheet and the amount of the discontinuity is equal to the density of 

 the sheet. 



Similarly across a magnetic current sheet the tangential component 

 of the electric intensity is discontinuous and the amount of this dis- 

 continuity is equal to the negative of the magnetic current density of 

 the sheet; thus 



£/ - £/' = - .1/,. (14) 



In deriving equations (2) it is also necessary to assume that g, /j. 

 and € are continuous throughout the region under consideration. 

 They have no meaning on the boundary between two different media. 

 Since the boundary is a geometric surface, it cannot constitute either 

 an electric or a magnetic current sheet. Hence the components of 

 E and H tangential to such a boundary are continuous across it. 

 These boundary conditions provide a link between the fields in the 

 two media. 



