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8/19/2019 T04 - ELEC 216-Sep 30
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Review of Orthogonal
Coordinate Systems
Fall 2014
ELEC 216 – Electricity and Magnetism
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What will be covered
• Basics
• Position vectors
• Line integrals in different coordinates
• Surface integrals in different coordinates
• Volume integrals in different coordinates
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Cartesian Coordinates
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Line Integrals
The line integral over a scalar field can be interpreted
as the area under the field carved out by a particular curve.
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Line Integrals
One interpretation of the line integral of a vector field is the amount of
work that a force field does on a particle as it moves along a curve.
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Line Integrals in Cartesian Coordinates
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Line Integrals in Cartesian Coordinates (cont.)
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Line Integrals in Cartesian Coordinates (cont.)
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Line Integrals in Cartesian Coordinates (cont.)
0
0.5
1
1.5
2
-1
-0.5
0
0.5
10
5
10
15
20
x-axisy-axis
z -
a x
i s
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Line Integrals in Cartesian Coordinates (cont.)
0
0.5
1
1.5
2
-5
0
54
4.5
5
5.5
6
z -
a x
i s
x-axisy-axis
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Surface Integrals
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Surface Integrals
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Surface Integrals
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Surface Integrals in Cartesian Coordinates
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Surface Integrals in Cartesian Coordinates
(cont.)
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Surface Integrals in Cartesian Coordinates
(cont.)
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Surface Integrals in Cartesian Coordinates
(cont.)
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Surface Integrals in Cartesian Coordinates
(cont.)
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Surface Integrals in Cartesian Coordinates
(cont.)
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Volume Integral in Cartesian Coordinate
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Volume Integral in Cartesian Coordinate
(cont.)
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Volume Integral in Cartesian Coordinate
(cont.)
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Cylindrical Coordinate
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Line Integral in Cylindrical Coordinate
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Line Integral in Cylindrical Coordinate
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Line Integral in Cylindrical Coordinate (cont.)
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Line Integral in Cylindrical Coordinate (cont.)
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Line Integral in Cylindrical Coordinate (cont.)
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Surface Integral in Cylindrical Coordinate
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Surface Integral in Cylindrical Coordinate
(cont.)
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Surface Integral in Cylindrical Coordinate
(cont.)
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Surface Integral in Cylindrical Coordinate
(cont.)
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Volume Integral in Cylindrical Coordinate
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Spherical Coordinate
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Line Integral in Spherical Coordinate
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Line Integral in Spherical Coordinate
(cont.)
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Surface Integral in Spherical Coordinate
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Surface Integral in Spherical Coordinate (cont.)
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Surface Integral in Spherical Coordinate (cont.)
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Surface Integral in Spherical Coordinate (cont.)
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Volume Integral in Spherical Coordinate
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Summary
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Summary
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Summary
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Summary
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Example
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Example