Lorentz force, force on conductors We generally say that Lorentz force acts on the charge particles. but when we keep a current carrying conductor in a wire, we say the wire experience a force. now how we explain it?
 A: The force acting on the wire is a macroscopic result (effect) of Lorentz forces acting on the charge carriers. This force belongs to class of ponderomotive forces, which means it acts on the heavy part of the wire, not just on the charge carriers.
In some sources (mainly French) this macroscopic force is called Laplace force. It is a useful term which should be used more in teaching, mainly to distinguish macroscopic forces on wires from microscopic forces on the charge carriers.


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*the Lorentz force acts on a current-forming charge carrier in the wire or when in vacuum; it is due to external magnetic field (relative to the particle) and it is a concept belonging to microscopic theories;

*the Laplace force acts on a piece of wire, it is due to internal forces from those charge carriers acting on the rest of the wire; the Laplace force can be thought of as secondary effect of the Lorentz forces acting on the charge carriers inside the wire.
A: Okay Lorentz force one of the primary constituents (not to be confused with constituent form of Maxwell's equations for non vacuum dielectric medium/permittivity etc) of Maxwell's equations for classical electrodynamics (with out sr or light speeds) is given (poorly) by wikipedia as $$F= q(E+v\times  B) $$
Where $F$ and $B$ are the respective electric and magnetic fields. You can see the electric contribution is just the regular electric field and really not part of Lorentz force but wikipedia include it.
So not to confuse Lorentz law or Lorentz field which ever you choose, force etc. is $$ F= q(v \times B)$$
This describes the force on a charged particle as a vector given the vector velocity and the present vector of the magnetic field. It's some the cross product. So you use the right hand rule where thumb is velocity, index finger is magnetic field line at point and the resulting index finger points the way the force is directed.
It is the primary description of the way classical non relatavistic electric particles interact with a magnetic field. 
Also now considering a wire isn't a charged mass, it is a conducting neutral charge metal classically. A Lorentz force thus wouldn't apply a significant force to the wire as a whole, but would induce a current. This is physics behind an alternator or generator, not a motor.
