Simple Alternating Current Motor

Introduction

            This document will discuss the physics of a simple alternating current (AC) motor.  Almost all of modern civilization relies on these and it is good for the viewer to understand how they operate. The particular type we are discussing is one where the rotor contains the conducting wires and the stator is made of a permanent magnet.

Figure 1:The components of the simple AC motor as viewed in cross section.  The magnetic field , B, in the gap points from the North pole (red) to the South pole (blue).

Physics

            The motor relies on the following force law:

 

                                                                                                                          (1)

where i is the current, L is the length of the wire (assumed straight here) through which that current flows, and B is the magnetic field vector of the permanent magnet.  The permanent magnet is color-coded so that the north pole (N) is red and the south pole (S) is blue.  In the gap B points from the red pole to the blue pole.  Therefore, relying on the right hand rule, when the wires on the right side have current flowing into the screen, the cross product in equation 1 indicates that the force, F, is downward. 

 

As can be seen by viewing the animation, the current direction switches sign when the average orientation of the wires is along the 12 o’clock and 6 o’clock line.  This is necessary because, otherwise, the torque direction would be reversed and the motor would just oscillate back and forth. Also, since the AC drive current is sinusoidal in nature, the length of the force vectors goes to zero when the drive current is zero as in the 12 o’clock-6 o’clock orientation.