A current carrying conductor is placed in a magnetic field experience a force , Why?

When a current carrying conductor is kept in a magnetic field then conductor itself produces magnetic field around it. Now there is the attraction and repulsion of magnetic field between external magnetic source and magnetic field created by conductor. Thus, conductor feels some force on it. 

The current carrying conductor generates it own magnetic field around it. ... When two magnetic fields interact there will be attraction and repulsion between them based on the direction of the external magnetic field and the direction of the current in the conductor. That is why the conductor experiences a force.The force on a current-carrying wire in a magnetic field is F = IlB sin θ.A current carrying conductor produces a magnetic field around it which interacts with the magnetic field in which it is held. Thus, it experiences a force. Direction of this force depends upon the direction of current and the magnetic field.

When a current carrying conductor is placed in a magnetic field, a mechanical force is exerted on the conductor which can make the conductor move.A larger current in the conductor will result in a larger force acting on it if the strength of the magnetic field is kept constant, as shown in Figure. The magnitude of the force on a current carrying conductor increases when the strength of the magnetic held is increased.Current is directly proportional to magnetic force for a straight current carrying conductor in a uniform magnetic field. ... If the current is doubled the force on the conductor will double. If the current is is reduced to a third of the initial value the force will also reduce to a third of its initial value.

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.