I dont believe that faradays law (which can be used to explain the voltage induced in a small constant current loop) distinguishes between a horizontal and a vertical part of the loop conductor. Coils, and a loop can be in a simplified model assumed as a 1-turn coil, are normally circular. What would you assume in a circlar loop conductor?
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With the earlier postet EZNEC model it should be possible to calculate the currents and their phase relations.
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maybe this document helps. pages 5, 22.
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regards
Fred