Torque equation of an electric motor

[fonz]

The example I am looking at in my textbook starts by considering and area of the rotor surface of width w and length L.

Then the axial current flowing in the width w is equal to I=wA which is exposed to a radial flux density B

So from the Lorentz force F=IBxL the equation becomes

F= wABxL

so the force per unit area is F/wL which becomes:

F=BA

Then to obtain the torque the force per area is multiplied by the entire area of the rotor (2∏rL) then multplied by the radius of the rotor

So the overall torque equation becomes:

T=BA x 2∏rL x r

What doesn't make sense is how can the current be equal to wA? by the Lorentz equation the force on a current carrying conductor is IBxL so the width and area of the conductor carrying the current I does not matter? so why does it apply here?

Regards
Dan

 

[technician]

I agree with you. Without seeing any diagram I would say the force on the side of the coil of length L will be BIL. The torque produced by the coil will be BILd where d is the separation of the sides of length L. Ld is the area of the coil.
If the coil is in a uniform field then the torque will be BIASinθ where θ is the angle between the field and the normal to the plane of the coil.
If the coil has N turns then the torqe is BNIASinθ
I don't understand what seems to be in your book !
hope this is some help