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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