8/25/2005 A Gallery of Vector Fields.doc 1/12 Jim Stiles The Univ. of Kansas Dept. of EECS A Gallery of Vector Fields To help understand how a vector field relates to its mathematical representation using base vectors, carefully examine and consider these examples, plotted on either the x-y plane (i.e, the plane with all points whose coordinate z=0) or the x-z plane (i.e, the plane with all points whose coordinate y=0). Spend some time studying each of these examples, until you see how the math relates to the vector field plot and vice versa. Remember, vector fields—expressed in terms of scalar components and base vectors—are the mathematical language that we will use to describe much of electromagnetics—you must learn how to speak and interpret this language!8/25/2005 A Gallery of Vector Fields.doc 2/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆ()xr=Aaˆ()yr=−Aa8/25/2005 A Gallery of Vector Fields.doc 3/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510yˆˆ()xyr=−Aaa-10 -5 5 10x-10-5510yˆ()xrx=Aa8/25/2005 A Gallery of Vector Fields.doc 4/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆ()yrx=Aaˆˆ()xyrx x=+Aaa8/25/2005 A Gallery of Vector Fields.doc 5/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆ() (10 )xrx=+Aaˆ() (10 )yrx=+Aa8/25/2005 A Gallery of Vector Fields.doc 6/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510yˆ() (10 )ˆ(10 )xyrxx=+++Aaa-10 -5 5 10x-10-5510y3ˆ() (10 )xrx=+Aa8/25/2005 A Gallery of Vector Fields.doc 7/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510y3ˆ() (10 )yry=+Aa33ˆ() (10 )ˆ(10 )xyrxy=+++Aaa8/25/2005 A Gallery of Vector Fields.doc 8/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆ()yry=Aa ˆ()xry=Aa8/25/2005 A Gallery of Vector Fields.doc 9/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆˆ()xyrx y=+Aaaˆˆ()xyry x=+Aaa8/25/2005 A Gallery of Vector Fields.doc 10/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆˆ()xyrx y=−Aaaˆˆ()xyry x=−Aaa8/25/2005 A Gallery of Vector Fields.doc 11/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510y-10 -5 5 10x-10-5510yˆ()ˆˆcos sinxyrρφφ==+Aaaaˆ()ˆˆsin cosxyrφφφ==−Aaaa8/25/2005 A Gallery of Vector Fields.doc 12/12 Jim Stiles The Univ. of Kansas Dept. of EECS -10 -5 5 10x-10-5510z-10 -5 5 10x-10-5510zˆ()ˆsin cosˆcosrxyrθφθ==+Aaaaˆ()ˆcos
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