Why does a current carrying conductor kept in magnetic field shift from its position?

The current carrying conductor kept in a external magnetic field shifts from its initial position due to attraction and repulsion between external magnetic field and that of the current around the wire. 

The magnetic field exerts a force on a current-carrying wire in a direction given by the right hand rule 1 (the same direction as that on the individual moving charges). This force can easily be large enough to move the wire, since typical currents consist of very large numbers of moving charges.Fleming's right-hand rule gives which direction the current flows. The right hand is held with the thumb, index finger and middle finger mutually perpendicular to each other (at right angles), as shown in the diagram. The thumb is pointed in the direction of the motion of the conductor relative to the magnetic field.

As it is carrying current (DC), some flux lines will be generated around the conductor and they are concentric with the central axis of the conductor. ... So an electromagnetic field is established due to this current through this conductor.We already know that stationary charges produce an electric field which is proportional to the magnitude of the charge. The same principle can be applied here, moving charges produce magnetic fields which are proportional to the current and hence a current carrying conductor produces magnetic effect around it.

The magnetic field inside a conductor with uniform current density J = I/πR² can be found with Ampere's Law. Inside the conductor the magnetic field B increases linearly with r. Outside the conductor the magnetic field becomes that of a straight conductor and decreases with radius.This process of generating current in a conductor by placing the conductor in a changing magnetic field is called induction. This is called induction because there is no physical connection between the conductor and the magnet. The current is said to be induced in the conductor by the magnetic field.