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You get zero voltage. The magnetic field lines are surrounding the wire in circles. To get an induced voltage, the coil axis must be parallel to the field lines, in other words oriented perpendicular to the wire, but not in it's plane, e.g. the coil besides the wire in a crossed position.
An ideal coreless AC current sensor has the form of a Rogowski coil. https://en.wikipedia.org/wiki/Rogowski_coil
Any AC current sensor does.but the Rogowski coil do induces the voltage..