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Unformatted text preview: Lecture 7 Notes, 95.658, Spring 2012, Electromagnetic Theory II Dr. Christopher S. Baird, UMass Lowell 1. Far-Field Dipole Radiation Review- Using the Green's function solution for radiation, we applied it to a localized source.- To find the far-field behavior of the waves, we then expanded the exponential and kept only the first term, which led to: A x ,t = 4 e i k r t r J x ' e i k r ' x x ' d x '- We further expanded the source into multipoles and found that electric dipole radiation in the far field is: A ( x ,t )= i 4 p e i ( k r t ) r where p = x ' (( x ' )) d x ' which leads to the fields: B = ck 2 p 4 ( k p ) e i ( k r t ) r E = c 2 k 2 p 4 k ( k p ) e i ( k r t ) r- The unit vector in the propagation direction used here must not be confused with the unit vector in the z direction, although they are labeled the same....
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