SourceObsR

SourceObsR - R (Source-Obs. Distance) in Cylindrical Coords...

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©B obY o rk Back to TOC R (Source-Obs. Distance) in Cylindrical Coords ˆ y ˆ z (,,) z   ˆ x z R r r z z 22 2c o s ( ) d    From law of cosines this length is: 2 2 2 () 2 c o s ( ) R dz z z z a b c 222 o s cab a b  d Law of cosines: Now use Pythagorean theorem to get R:
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©B obY o rk Back to TOC R (Source-Obs. Distance) in Spherical Coords ˆ y ˆ z (, , ) r   ˆ x r R r r 22 ( sin ) ( sin ) 2 sin sin cos( ) dr r r r    From law of cosines we get:  2 2 () ( c o s c o s ) 2s i n s i n c o s ( ) c o s c o s 2c o s Rd z z d r r rr r r r r d Now use Pythagorean theorem to get R: cos zr cos See next page
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©B obY o rk Back to TOC Cos γ ˆ y ˆ z ˆ x R r r In some cases it is helpful to know the angle γ subtended by the source and observation points ˆˆ cos rr  cos sin x yz z  
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This note was uploaded on 12/04/2010 for the course ECE 134 taught by Professor York during the Fall '08 term at UCSB.

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SourceObsR - R (Source-Obs. Distance) in Cylindrical Coords...

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