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I'm trying to find the mutual inductance of a straight wire and a square conductor. I used the integral $\int B \cdot da=Φ=ΜI$

However,M comes out negative. Does this have a physical meaning or did I just miscalculate?

The current in the square flows as shown and the wire is supposed to be on the z axis with the current going up.

enter image description here

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  • $\begingroup$ Show a diagram. $\endgroup$
    – DanielSank
    Jun 2, 2017 at 15:51

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There is no reason for a mutual inductance to be positive, all depends on relative orientations of the conductors and on prescribed directions of currents.

enter image description here

For example, on the top picture a current in the left coil will create a positive magnetic flux in the right coil, thus the mutual inductance is positive. "Positive magnetic flux" means the magnetic field direction is related to a prescribed direction of a current in the right coil by the right hand screw rule.

On the bottom picture the right coil is flipped, hence the mutual inductance is negative because a current in one coil will create a negative magnetic flux in the second coil.

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