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In the proof of Babine's principle, we argued that the tangential magnetic field produced by an electric current element is zero in any plane containing

In the proof of Babine's principle, we argued that the tangential magnetic field produced by an electric current element is zero in any plane containing the current element. How would I show a mathematical proof that an arbitrary planar electric current of finite support produces not tangential magnetic field in a region of the plane not occupied by the current?

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