Problem: Current is distributed in a non-uniform way. How to measure or integrate the current value over only a part of the area?

Solution: Use line integral.

Example: There is a round wire with non-uniform current distribution due to skin effect and proximity effect. We are interested in the current only in the upper half of the circular wire. It might be needed to add a “dummy” point at the centre, because otherwise an arc will be drawn, not a straight line.

The red contour line was drawn by left-clicking (left click snaps to a point) on the left-most point, then left-click on the central point, left-click on the right-most point, and then series of RIGHT-clicks (right click allows arbitrary position, not snapped to a point) to go through the air and circle back to the original point, and the left-click again on the start point (left-most in the circle).

This produces a closed contour, which can be then integrated for the H*t value, and the upper value in the pop-up output window gives MMF in the unit of ampere-metres. If the block of conductor is solid then the number of turns = 1, and therefore MMF = current in amperes, enclosed by the contour.

In the example, the calculation gives 0.6785 A, for the total current in the conductor of 1.0000 A. It is clear from the distribution that higher current flows in the upper half of the circular conductor.

Note: it is more accurate to integrate through air in this case, rather than along the edge of the wire, because the integral is somewhat more accurate. Integrating over the whole wire along the edge gives 0.9365 A. But drawing a closed contour in the air around the wire gives 1.0006 A.