EM_scattering_homework_1_solution

Let e e s s be the scattered field generated by the

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Unformatted text preview: s , � sin �s � � θs , � � sin �s ,cos �s ,0 � � ˆ s (1.13) ˆ φs ˆ ks ˆ θs z �s h y �s x 2a kˆi � zˆ ˆ E i0 � E 0 x Problem 3: Consider a plane wave traveling in free space. The wave is incident upon a certain dielectric object of arbitrary shape with a dielectric constant � � r � generating equivalent currents inside the object. Let E s , H s denote the scattered field, i.e., the field induced by these equivalent currents. In the far field zone the scattered electric field is given by: E sf (r ) � exp � � jkr � ˆ Q � kˆs , k i r � � � ˆ ˆˆ W here k � � � 0 �0 , k s denotes the direction of scattering and Q � k s , k i � is the vector scattering amplitude (see the powerpoint slides for a description). Using the reciprocity theorem of electromagnetic theory show that k� � ˆˆ ˆ e0 � Q� ks , ki � � e0 � � n � E s � r � � exp � jks � r � dS � � 4� j � � � S � � � ˆ� h0 � � � H s � r � � n� exp � jks � r � dS � � � S ˆ ˆ W here e0 is any arbitrary constant vector with ks � e0 � 0 , and h0 � � �1/ � � ks � e0 , � � �0 / � 0 , and S is any arbitrary closed surface surrounding the object. (See figure...
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This note was uploaded on 02/26/2013 for the course EE 25227 taught by Professor Akbabi during the Spring '13 term at Sharif University of Technology.

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