The Method of Moments in Electromagnetics

A Brief Review of Electromagnetics 17½Ö ¾ ½Ö ¿ etc., because of the differential operators. In the far field we expect thatonly those fields varying according to ½Ö will have significant amplitude. Thesecomponents behave like a plane wave with no components along the direction ofpropagation. The far electric field will therefore be computed asand the magnetic field obtained from the electric field asE´rµ A´rµ (2.99)H´rµ ½ r ¢ E´rµ (2.100)where we have assumed the field to be a plane wave propagating along the vector r.2.5.2.1 Three-Dimensional Far FieldWe can write the expression for the far-zone electric field by using (2.98) with (2.99),resulting in the well-known expressionE´rµ Ö ÖÎJ´r ¼ µ r¼ ¡r r ¼ (2.101)For scattering problems with an incident field E and scattered far field E × , the threedimensionalradar cross section ¿ is defined as [1] ¿ Ö ¾ E× ¾E ¾ Ö¾ E × ¾ (2.102)where it is usually assumed that E ½for computational convenience.2.5.2.2 Two-Dimensional Far FieldIn two dimensions the radiated far electric field is given byE´µ A´µ J´ ¼ µÀ ´¾µ¼ ´ ¼ µ ¼ (2.103)Using the large-argument approximation of the Hankel function [4]×À Ò ´¾µ ´µ ¾ Ò ½ (2.104)and (2.98) we write×¾¼ ´µ ¼ ¡À ´¾µ(2.105)