Spherical Polar Coordinates

In Fig. A6.1, the spherical polar coordinates (aka polar coordinates) r, θ and ϕ are given by: where The volume element dτ in Fig. A6.1 corresponds to the infinitesimal quantity dxdydz in Cartesian coordinates; it is straightforward to show the relationship: The limits of the polar variables that correspond to x, y and z each between − ∞ and + ∞ are: Convert the following Cartesian coordinates to spherical polar coordinates. (Answer at end of Appendices.)