The correct answer is: D. all of the above.
The size of a synchronous motor decreases with the increase in flux density, horsepower rating, and speed. This is because the torque produced by a synchronous motor is proportional to the product of the flux density and the current. The current is proportional to the horsepower rating, and the flux density is proportional to the speed. Therefore, as the flux density, horsepower rating, or speed increases, the torque produced by the motor increases, and the motor can be made smaller.
Flux density is the magnetic field strength in a region of space. It is measured in teslas (T). The higher the flux density, the stronger the magnetic field. The stronger the magnetic field, the more torque can be produced by the motor.
Horsepower rating is a measure of the power output of a motor. It is measured in horsepower (hp). The higher the horsepower rating, the more power the motor can produce. The more power the motor can produce, the more torque it can produce.
Speed is the rate at which a motor rotates. It is measured in revolutions per minute (rpm). The higher the speed, the faster the motor rotates. The faster the motor rotates, the stronger the magnetic field. The stronger the magnetic field, the more torque can be produced by the motor.