For steady currents in vacuum, Ampère's circuital law is
Here is an oriented closed curve, its tangent line element, and the signed electric current through a spanning surface oriented by the right-hand rule. A circular contour about a straight infinite wire has constant tangential magnetic field, so . The Lorentz force on a length of the other wire is . Therefore
The right-hand rule makes the force on each parallel, same-direction current point toward the other wire.

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