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Unformatted text preview: x ). But how to memorize f ( x, z )? Here’s a graphical way with an interesting physical interpretation. Let an electrical charge q be located at a point with polar coordinates ( r, θ ) (here, θ is the angle between the radius and the y-axis) with r < 1. In physics one shows that the potential at the point with polar coordinates (1 , 0) on the y-axis is proportional to 1 /r where r is the distance between this point and the point where the charge is: potential ∼ 1 r . * MAP 4305; Instructor: Patrick De Leenheer. 1 q r r ’ theta 1 Now by the law of cosines: ( r ) 2 = 1 + r 2-2 r cos( θ ) , and thus the potential is proportional to: 1 p 1 + r 2-2 r cos( θ ) , which is exactly f (cos( θ ) , r ). 2...
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
- Summer '06