where St is the entire cross-sectional area of the winding,
and I is the current through one turn of the winding. Equation
(3) offers a simpler computation by avoiding the tedium
of multiturn calculations. In particular, the current
density vector J includes the signs of the currents. The
flux linkage integration for a winding is given by a uniform
formula, leading to a simpler calculation. The integration
in (3) also can be performed by a command or a
“verb” in many FE packages. However, if the winding
carries no current, (3) is no longer valid unless the winding
is assigned a small “dummy” current. This
“dummy” current should be small enough that the original
magnetic field is not significantly disturbed. It should
be noted that “dummy” currents will add errors to magnetic
potential solutions, and thus to the inductance evaluation.
Also, (3) is not recommended for inductance calculations
involving those windings that carry no current