It is useful to learn about other coordinate systems. For example, to solve a problem involving a cylindrical shape like electromagnetic fields on a rod, you should use a cylindrical spherical coordinate system. For problems involving a sphere, like electromagnetic fields of a sphere, you should use spherical coordinate systems.
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Cylindrical Coordinate System
Cylindrical coordinates add the Z dimension to the polar coordinates (r, θ). It's dimensions are (r, θ, z) which are radial, azimuthal, and vertical axes.
| From cartesian to cylindrical: | From cylindrical to cartesian: |
| x = r*cos(θ) | r²= x² + y² |
| y = r*sin(θ) | tan(θ)=y/x |
| z = z | z = z |
Spherical Coordinate System
Spherical coordinates are (r, θ, φ) which are radial, azimuthal, and vertical axes.
| From cartesian to spherical: | From spherical to cartesian: |
| x = r*sin(θ)cos(φ) | r²= x² + y² + z² |
| y = r*sin(θ)sin(φ) | cos(θ)=z/r |
| z = r*cos(θ) | tan(φ) =y/x |
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