Snapshot 1: the 10mm-diameter nonmagnetic wire carries
Snapshot 2: the 10mm-diameter nonmagnetic wire carries
Snapshot 3: the 10mm-diameter ferromagnetic cylinder of
The resultant field both inside and outside the cylinder can be obtained considering the vector potentials of the uniform field
and the wire current
. As the result, the field is described in the following equations in cylindrical coordinates
is the radius of the cylinder (or
, using a wire of diameter
). The third component
is zero. Those fields are transformed to Cartesian in the graphics displayed.
For Snapshots 1 and 2, the magnetic field at the wire surface due to the wire current
is calculated to be
, respectively. Since
in those examples, they correspond to the cases
. The unsymmetrical field patterns suggest that an upward electromagnetic force should be generated.
Snapshot 3 shows the effect of an outside magnetic field on the ferromagnetic material. According to the above equation, the field inside the cylinder is
, with direction along the
axis, the direction of the applied field. The field intensity is very small since
 J. A. Stratton, Electromagnetic Theory
, New York: McGraw–Hill, 1941.