This is a summary of the Electrical Apparatus April 2007 featured technical article,  by Richard L. Nailen, P.E.

Magnetic fields are easily analyzed when the air gaps through which they pass are uniform. Variations in shape, however, such as at the edges of field poles in a synchronous motor or generator, cause distortions in the field that require a technique known as field mapping or “flux plotting” to determine how the distorted field will cause flux density to vary throughout the region.

The mapping is done in two dimensions so chosen that the field is uniform in the third dimension. The process involves first drawing typical lines of force throughout the region of interest on a two-dimensional picture (drawn to scale) of the area involved. The pattern of such lines becomes visible in the classic science experiment of sprinkling iron filings on a sheet of paper atop a bar magnet.

Each such line must enter and exit magnetic material at 90 degrees, because otherwise a vectorial component of magnetic force would have to exist parallel to the material surface, implying a variation in magnetomotive force along that surface.

The drawn lines are spaced to form squares, as nearly as possible, with internal angles of 90 degrees. Because their sides are generally curved, they’re known as “curvilinear” squares. Where the air gap increases, the squares become larger. Because the same amount of magnetic flux passes across the gap through each square, flux density averaged across each square is inversely proportional to square width. Accuracy of the plot–and hence of the flux density variation derived from it–will increase as it is further subdivided into smaller and smaller squares, by adding more flux lines and crossing them by “equipotential” lines (on which each point is at the same relative magnetomotive force level) bisecting them.

The same mapping technique is useful in analyzing electric fields, as in the determination of dielectric stress concentration at the ends of a cable shield, or in the air between a cable and its enclosing raceway. The relationships between lines of electrostatic force and relative electric field strength are analogous to those involved in magnetic fields. Heat transfer and fluid flow analysis can also be done this way. designs