Electromagnetic force in electric motor

batsan

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?

Meir Achuz

There is B in the groove.

batsan

Are you sure?
The magnetic resistance of the groove materials, such as copper, insulation ,air etc is many times more then steel. The magnetic flux pass around the groove, but not inside it.

Meir Achuz

The hig magnetic reluctance (not resistance) of those materials is what permits the B field to enter the groove. That is why steel is not used for the armature.

batsan

Ok. Is this correct picture or not?
http://www.mfly.de/animation_b.gif

Meir Achuz

The picture is colorful, but I don't think it is relevant to your question or my answer.

batsan

Yes,this is AC motor, but formula for its force must be the same. As we see color of groove is blue and it corresponds to B=0.

Meir Achuz

The picture is colorful, but I don't think it is relevant to your question or my answer, since B is not zero in the groove however they color it.