Does the energy of a magnetic field decrease when it moves a conductor carrying a current? When a charged particle moves in an electric field, the field performs work on the particle. Thus, the energy of the field decreases, turning into kinetic energy of the particle.
Does the magnetic field of a permanent magnetic similarly lose energy and perform work when moving a conductor with a current?
 A: Magnetic forces do not perform work because they are always perpendicular to the motion of the charged particle they act on.  However, it is possible to transform the energy stored in a magnetic field into the bulk motion of a conductor carrying a current.  I'll give one heuristic.
Consider two long wires running parallel.  Give them currents running in the same direction, and hold the wires still for a time that's long compared to the distance between them divided by the speed of light.
Now there is a magnetic field from the first wire at the location of the second and vice versa.  The wires attract each other.  Once released, they experience an acceleration towards each other.
However, this analysis only holds up until the first moment the wires are released.  After that, they are moving towards each other.  This motion of the wires entails a motion of the charge they carry - a current.  We will need to account for this current.
Say the wires run horizontally on your computer monitor, and the current is to the right.  Then the top wire is pulled down, and its current is now mostly to the right and a little bit down.  The magnetic field it feels is pointing towards you, out of the monitor.  Thus, the force on this top wire points mostly down, but it also points a little bit backwards.
Similarly, the force on the bottom wire is mostly up, but also a little bit backwards.  The backwards components of the magnetic forces act to decrease the currents in the wires.  If  the currents in the wire decrease, the magnetic field gets weaker.  In this way energy from the magnetic fields gets converted into the bulk motion of the wires carrying the currents.
The magnetic forces did not actually do any of the work here, though.  In the absence of any wire, the charged particles in the magnetic field would like to move in circles.  Instead, electrical forces between the particles and the wire they're trapped in forced the particles to stay inside the wire instead.  These electrical interactions between the charged particles and the rest of the wire did the work that accelerated the wires towards each other.
A: The electrons have charges and these have spins and these spin constitutes in part with the evolution of magnetic flux and so as these electrons move in the magnetic field, by faradays law and lorentz it experience a force proportionately with the amount of charges and its geometric position and others. This precisely is what happens in the linear accelerators, in the crt of tvs and mri machines and what have you, in fact it constitutes the principle behind the operation of the conventional electric motor.
in the motor, the continuous reversal of repulsion between the like poles (nort vs north and south vs south) with the aid of the commutator or slip-rings which makes the motor continuousley revolving round in circle or revolving against it's axis of rotation.
as to the question of whether the electric field or the magnetic field losses it's energy i don't think it is. The particle was the one moved by virtue of interacting with the field as the field is conserved. This particle acquires energy of motion thus kinetic energy when the field gives it the input force required to put it in motion.
A: There is no magnetic field - that is just a mathematical model implemented by Maxwell to facilitate calculations. There are only electric fields in reality - read up on Weber-Ampere electrodynamics.
