Hendrik Lorentz found that a charge moving in a magnetic field, in a direction other than the direction of the magnetic field, experiences a force. It is called Lorentz Force. Since current is due to the motion of charge, therefore a conductor carrying moving charges (or current) places in a magnetic field, in direction other than the direction of magnetic field, will also experience a force.
The direction of force on a current carrying conductor placed in a magnetic field is obtained by Fleming's left hand rule.
Fleming's left hand rule: Stretch the forefinger, middle finger and the thum of your left hand mutually perpendicular to each other. If the forefinger indicates the the direction of the magnetic field and the middle finger indicates the direction of flow of current, then the thumb will indicate the direction of motion of conductor.
If the conductor is free to move, it will start moving in the direction of the force.
Thus, if a current carrying conductor is placed in a magnetic field, it experiences the Lorentz force (unless the angle between the flow of current and magnetc lines is 0°).
With current flowing in the wire, the magnet pushes the wire away from the magnet because a force is exerted on a moving charge (or current) in a wire moving perpendicular to a magnetic field. A magnetic field exerts a force on a current-carrying wire. The direction of that force depends on the direction of current flow and the orientation of the magnetic field according to the right-hand rule.
Well imagine a magnetic field move between two wires,guess what, it produces electricity,so it should be the invers now,what happen to the magnetic field if a wire carrying current,moves in a magnetic field,it makes the magnetic field wharp or move.
You can check this by yourself by making an electromotor,its Faradejs work, who invented this really usefull theorem,he worked on it for almost 10 years.
Hope this Helps.
If a current carrying wire passes through an electromagnet area, then there will be a magnetising force that will either repulse or attract the wire. if the wire is around en iron, nickel or colbat core, then the magnetising force will be bigger.
Hope it has helped, but i doubt it because the others up before me really know what they are talking about.