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Below is the example of a rogowski coil so you have the big picture of my question.

In the picture, the current conducting wire (with current Ip) is encircled by a big circular loop rogowski coil. The cross sectional area of the winding itself can be a circle, rectangle, or oval.

For this variations of cross sectional area, I know how to calculate the mutual inductance.

However, what if the shape of the big loop is rectangular? How to calculate the mutual inductance?

I hope you all can help me figure this out.