Unformatted text preview: Systems
• Summary of Coordinate Systems Prof Joshua LeWei Li, EM Research Group
Prof 12 EE2011: Engineering Electromagnetics
Electromagnetics Coordinate System
Transformations
• Summary of Coordinate Transformations Prof Joshua LeWei Li, EM Research Group
Prof 13 EE2011: Engineering Electromagnetics
Electromagnetics Summary
• Why do we use more than 1 coordinate system?
ˆˆˆ
• Why is it that the base vectors (x, y , z ) are
ˆ
independent of the location of a point, but r and ˆ
are not?
• What are the cyclic relations for the base vectors in
(a) Cartesian coordinates, (b) cylindrical coordinates,
and (c) spherical coordinates?
• How is the position vector of a point in cylindrical
coordinates related to its position vector in spherical
coordinates?
Prof Joshua LeWei Li, EM Research Group
Prof 14 EE2011: Engineering Electromagnetics
Electromagnetics Lecture 1: Review of Vector
Calculus – Part II
• Gradient of a Scalar Field
– Gradient Operator in Cylindrical & Spherical
Systems
– Properties of a Gradient Operator • Divergence of a Vector Field
– Divergence Theorem Curl of a Vector Field
– Vector Identities Involving the Curl
– Stokes’s Theorem • Laplacian Operator
Prof Joshua LeWei Li, EM Research Group
Prof 15 EE2011: Engineering Electromagnetics
Electromagnetics Vector Line Integrals
F dl FA dl
A FB dl FC dl B C FA A FB B FC C F vector field vector line FA FB FC ABC y C
A
FA
15a B FC
x FB Example
FA 4x
ˆ FB 2y
ˆ FC 7z
ˆ F dl A 3x
ˆ
B 4y
ˆ
Cz
ˆ FA dl
A FB dl
B FC dl
C FA A FB B FC C
12 8 7
27 1...
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Full Document
 Spring '14
 Electrical Engineering, Vector Calculus, Coordinate system, Polar coordinate system, Vector field, Prof Joshua LeWei Li

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