Vector fields in cylindrical and spherical coordinates

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space. When these spaces are in (typically) three dimensions, then the use of cylindrical or spherical coordinates to represent the position of objects in this space is useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with round cross-section, heat distribution in a metal cylinder, electromagnetic fields produced by an electric current in a long, straight wire, accretion disks in astronomy, and so on.

Source: Wikipedia — Vector fields in cylindrical and spherical coordinates (CC BY-SA 4.0)