notes6 2317 - Review of Coordinate Systems ECE 2317 Applied...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 6 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Review of Coordinate Systems Review of Coordinate Systems x y z r P ( x,y,z ) An understanding of coordinate systems is important for doing EM calculations. Rectangular Rectangular ± ± rx x yy zz =++ ± Short hand: ( ) ,, y z = Book: xyz ra x a y az dx dy dz dS = dxdy dS = dxdz dS = dydz dV dx dy dz = x y z r P ( x,y,z ) Rectangular (cont.) Rectangular (cont.) ± ± dr xdx y dy zdz ± Path Integral (need dr ) ± ± x ± Note on notation: dl is often used instead of dr x y z A B C dr r r +dr
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Cylindrical Cylindrical . x y ρ φ () 22 1 cos sin tan / x y zz xy y x ρφ = = = =+ = = x y z . z P ( , , z ) Cylindrical (cont.) Cylindrical (cont.) Unit Vectors Note : and depend on ( x, y ) l ± x l y ± x y z . l ± z ± l ± ± ± ± ± l ± l ± 12 1 1 cos cos xA x y x Ax x A ⋅= ⋅+ =⋅ = Expressions for unit vectors l ± 2 cos 2 sin Ay π ⎛⎞ =− ⎜⎟ ⎝⎠ = Hence l ± ± cos sin φφ x y l ± l ± ± A y Assume Similarly, Then we have: Cylindrical (cont.) Cylindrical (cont.) l ± ± ± ± ± ± l ± ± l ± cos sin sin cos cos sin sin cos x y + Summary of Results Cylindrical (cont.) Cylindrical (cont.)
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Differentials x y z dS = ρ d d φ dS = d dz dS = d dz d d dz dV d d dz ρρφ = Note: dS may be in three different forms Cylindrical (cont.) Cylindrical (cont.) x y d x y z dz l dr d = ± () dr d φρφ = dr
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This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.

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notes6 2317 - Review of Coordinate Systems ECE 2317 Applied...

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