EDGE : Force on current carrying conductor

Our experiment contains a horseshoe magnet and a conductor which is free to move to and fro inside a magnetic field generated by the horseshoe magnet. As soon as we switch on the battery and the current flows through the conductor, it starts moving towards the left. So let's see why this happens. When we pass the current through the conductor, it generates the magnetic field around it. When this magnetic field interacts with external magnetic field produced by the magnet, it tries to align with it which in turn produces a force which moves the conductor. The current flows through the conductor from point A to point B. The magnetic field is in the downward direction. So if we align the forefinger in the downward direction and the middle finger in the direction from A to B, then the thumb points towards the left. So the force exerted on the conductor should be towards the left, which is the same as we observed in our experiment.