496 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



dy 



= iwD:c + J> 



— — - = lOiDy + Jy, 



ax 



dKy dEx 

 dy 



dx 



= — io)Bi 



dDx , dDy 



dx dy 



(ii-i) 



(n-2) 



(II-3) 



(n-4) 



In these equations H, B, D, £, / and p all have their usual meanings. A 

 positive time factor e*"' has been introduced. 



Y 



■♦►x 



Fig. 3 — Rectangular coordinate system. 



Let us for the moment suppose that we are dealing with an anisotropic 

 medium such that the following relations exist: 



Jx — Cx Eix 5 Jy — (Ty Ey 



Dx ^ €x Ex 5 Dy = €j/ Ey 



B, = ^ioHz 



(11-5) 

 (II-6) 

 (11-7) 



Here the a's are conductivities, the e's dielectric constants, and no is the 

 permeability of free space. Suppose also now that the fields all vary with x 

 according to a factor g-^^^. If k has a positive real part we will be dealing 

 with a wave moving along the a;-axis in a positive direction, and a negative 

 imaginary part will indicate that this wave is attenuated. 



Using the above relations, one can easily find the following equations: 





ioi^x + (Tx 



Ut3€y + (Ty 



Ex = 



[tWHO (Ty 



1 



ua€x H" ffx dy 



ik 



CoVo iy + k ]Hz 



dIL 



Ey^ . , 



tO)€y -j- (Ty 



H. 



(II-8) 



(11-9) 



(11-10) 



