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brandon_1892

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With Cauchy's Integral Theorem, if a function is analytic on and in the loop integrated over, $$\oint_C f(z) dz = 0$$; otherwise there may be a nonzero result.

Since essentially the magnetic field approaches infinity right in the current, I thought maybe Ampere's Law is an instance of Cauchy's Integral Formula/Theorem; when there is no current enclosed, the magnetic field has no such center, so all of it would be analytic.

Is this an actual connection, then?