If the magnetic field affects charged particles in movement, then it must also affect a conductor through which a current is flowing. The charged particles moving through it will be pushed in some direction by the field. As they are confined inside the conductor, they will exert a measurable force on it.

   In the visual , you can observe the effect of the magnetic field on a straight cable. If the conductor is curved, or if the field is not homogeneous, then it is necessary to imagine the conductor is composed of an infinite number of small straight fragments of length dL and add up (integrate) the forces acting on each and every one of them.