Final answer:
Two perpendicular, non-touching, current-carrying wires exert force on each other, directed along their lengths as determined by the right hand rule. There is no net torque exerted by one wire on the other as there is no lever arm created by the force.
Step-by-step explanation:
When considering two long straight wires that run perpendicular to each other without touching, we must refer to the principles of electromagnetism to determine if there is a force or torque acting on one another. According to Ampere's law and the Biot-Savart law, a current-carrying wire creates a magnetic field around it. The direction of the magnetic field can be determined using the right hand rule, where one points the thumb in the direction of the current and the curling fingers show the direction of the magnetic field lines.
If another current-carrying wire is placed in this magnetic field, it will experience a force due to the interaction of its own current with the magnetic field created by the first wire. This force is perpendicular to both the direction of the current and the magnetic field lines according to Fleming's Left-Hand Rule. In the case of two perpendicular wires, the current in one wire would be at a right angle to the magnetic field produced by the other, resulting in a force exerted on it. This force will be directed according to the right hand rule, meaning for each wire the force will be along the wire itself, directed inwards or outwards of the intersection point, depending on the direction of the currents in both wires.
As for torque, since the wires do not touch and the force is directed along the length of the wire, there is no lever arm to produce a torque. Hence, one wire does not exert a net torque on the other.