for electric motors
F= B I l
where B is magnetic field strength, I is current and l is length of wire perpendicular to the magnetic field
pretty sure in all application that magnetic field strength is proportional to current and is proportional to number of turn in the coil. (not 100% sure what ampere turns are sorry).
i.e. double amount of turns double magnetic field strength (in terms of a solenoid)
The magnetizing force is usually called the H field, and is typically
measured in ampere turns. The resulting magnetic field is usually called the
B field, and is typically measured in Teslas or Gausses.