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# Class Note for ECE 6341 with Professor Jackson at UH

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COURSE
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KARMA
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This 14 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15
ECE 6341 Spring 2009 Prof David R Jackson ECE Dept Notes 14 Addition Theorem Allows us to shift the origin for line sources Addition Theorem cont wZ H zkR Ripp39i lb This is the exact solution but it is not very useful Addition Theorem cont Assume 39 0 for simplicity Tube of current model y y 2 2 muo x K puo x 39 J10 39 0 p p Surfacecurrent Jsz 39A15 39 Addition Theorem cont Determine11 JJSZ 39p39d 39IO Jszlt 39gtA16lt 39gt so Alp39zlo Hence Using the tube of current concept JSZ 15 39 i cneW Addition Theorem cont 1 27 39 71 39 ggfkwp1d 0 1 w 539emd39 2 JP i 27rp39 tube of current X Addition Theorem cont W1 Z anejn Jn W2 Z bnej H52kp From previous derivation a 039 1 I0 27rp Addition Theorem cont Therefore we have an J Hf W I b J39 J W Hence Addition Theorem cont For 39 O replace gt 39 WI jluTIO 1 Hf kppejn VJn kpp 00 7 39n 39 wz J 40 Jnkpp 6 5 gtHn2kpp y 0 2 p0 ZKNWW x q 10 39 J 0 Addition Theorem cont Comparing with the original expression for the potential of the line current we have i0 H152 kp39Jn kpejn 39 0 lt 039 H02kI I v no Z J kaHn2 kp ejn 39 p gt 039 This is the addition theorem It also holds if k is replaced with kp Scattering From a Line Current Scattering From a Line Current cont wt 2 i0 Hnlt2gt kpv J kp ejnlt 39gt J nz oo This is only valid for 0 lt 039 Assume Ms 2 if i an H152 k p grew 2539 J nz oo This is valid for 0 Z a Scattering From a Line Current cont Boundary Conditions wsa9 az Wiaa az Hence anH ka H2gt W 39gt J lea or Scattering From a Line Current cont Final result s y 00 Hn2k039 2 WW w TZ mj ka H W 0 I scattered eld gt y 4 A x 0

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