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Spherical Coordinate

A vector in the spherical coordinate can be written as:

A = aRAR + aθAθ + aøAø, θ is the angle started from z axis and ø is the angle started from x axis.

The differential length in the spherical coordinate is given by:

dl = aRdR + aθ ∙ R ∙ dθ + aø ∙ R ∙ sinθ ∙ dø, where R ∙ sinθ is the axis of the angle θ.

The differential area of each side in the spherical coordinate is given by:
dSR = R2 ∙ sinθ ∙ dθ ∙ dø
dSθ = R ∙ sinθ ∙ dR ∙ dø
dSø = R ∙ dR ∙ dθ
The differential volume in the spherical coordinate is given by:

dv = R2 ∙ sinθ ∙ dR ∙ dθ ∙ dø


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