Sign of the Partial Inductances

The partial self inductance is always a positive quantity. The partial mutual inductance may be positive, negative or zero depending upon the polarity of the inductive voltage drop produced on the observation current path by the source path. If the two paths have the same orientation, the mutual inductance is positive.

Now suppose we exchange the locations of the source and sink terminals on one current path, so that the two current paths have the opposite orientation. The mutual inductance will now become negative. In the partial inductance example above, the loop inductance would be given by the modified formula:

L_total = L_P11 – L_P12 – L_P21 + L_P22

This of course gives the same result as before, because the signs of the partial mutual inductance terms have changed.

Finally, suppose we take one conductor and turn it 90 degrees relative to the other. The mutual inductance will become zero.