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Is there any kind of geometric pitch or config (right triangle, equilateral triangle, etc.) a system of three conducting wires carrying current in the same direction may be arranged so at least one of the wires does not have net magnetic force?

Assume that currents flowing through the wires are all different.

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Yes. Make them coaxial. Usually coaxial cables have two conductors, but there is no reason you couldn’t make one with three. Regardless of the currents, by symmetry there can be no net force.

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