Convert a scalar field from polar to Cartesian coordinates:

Change a vector field from Cartesian to polar coordinates:

Transform a scalar field:

Convert a spherical unit vector to Cartesian coordinates:

Convert the vertical unit vector to prolate spheroidal coordinates, specifying both metric and coordinate system:

Convert a rank-2 tensor from polar to Cartesian coordinates:

Re-express spherical harmonics in Cartesian coordinates:

An electric dipole of dipole moment located at the origin and aligned with the axis has the following electric potential in spherical coordinates:

Compute the corresponding expression in Cartesian coordinates:

Derive the dipole electric field in spherical coordinates:

Transform this expression to Cartesian coordinates:

The same expression is obtained by differentiating the Cartesian potential function:

Plot the lines of force in the plane:

Use Map to transform a list as a list of scalars rather than as a vector:

The same principle applies to lists of vectors and higher-rank tensors:

TransformedField changes the coordinate expressions for fields:

CoordinateTransform changes the coordinate values of points: