Leakage of a magnet flux of an electromagnet is considered to shorten a mag
net gap length effectively which dominates a strength of a magnetic flux de
nsity in an iron core. Because a transient eddy current occurs inside a cor
e, its time constant becomes longer when the leakage is larger. In addition
,the leakage is larger when the permeability of an iron core is larger. On
the other hand, Faraday's law which induces an eddy current includes a time
derivative of a flux density. Therefore an incremental permeability which
is a field derivative of the flux density is considered to dominate a time
constant of a transient eddy current. Consequently the time constant can ha
ve various values depending on excitation field levels due to hysteresis ch
aracteristics. The analytical expression for a transient eddy current is fo
rmulated by two-dimensional simultaneous Laplace's transformation for space
and time. This expression makes clear that a transient eddy current causes
a spatial distribution of a flux density both at a gap and inside a core w
ith a long time constant.