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16.360 Lecture 14

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16.360 Lecture 14. Today. Orthogonal coordinate systems. The Cartesian (rectangular) coordinate system The cylindrical coordinate system The spherical coordinate system. 16.360 Lecture 14. Cartesian coordinate system. z. dl. . . y. x. 16.360 Lecture 14.

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16.360 Lecture 14

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  1. 16.360 Lecture 14 • Today Orthogonal coordinate systems • The Cartesian (rectangular) coordinate system • The cylindrical coordinate system • The spherical coordinate system

  2. 16.360 Lecture 14 • Cartesian coordinate system z dl   y x

  3. 16.360 Lecture 14 • Cartesian coordinate system z directions of area y x

  4. z y x 16.360 Lecture 14 • Cylindrical coordinate system

  5. z y x 16.360 Lecture 14 • the differential areas and volume

  6. 16.360 Lecture 14 Example: cylindrical area z 5 3 60 y 30 x

  7. 16.360 Lecture 14 • Spherical coordinate system

  8. 16.360 Lecture 14 • differential volume in Spherical coordinate system

  9. 16.360 Lecture 14 • Examples (1) Find the area of the strip (2) A sphere of radius 2cm contains a volume charge density Find the total charge contained in the sphere

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