Suppose we have a DC motor with permanent magnet. Moreover, the armature of motor is groove rotor. The elementary electromagnetic force is given by: dF=jxBdv, where j is electric current density , x is vector multiplication , B - magnetic flux density , dv - elementary volume. If we integrate by all the volume, we will calculate only zero, because there is current density j in the groove , but there is no magnetic field B. Otherwise ,there is B in the steel , but no j. How you can explain that?