Throttling Mechanisms in Homopolar Motors
Fig. 1 depicts the essential elements of a homopolar motor. The battery is the seat of a CW emf around the circuit. Conduction electrons, flowing radially outward in the probe, experience magnetic forces into the page. The one-piece magnet-probe assembly begins to rotate CCW (viewed from above).
A Homopolar Motor
Let us first consider the case where the magnet is a conductor. As previously pointed out, such a magnet engenders zero net E field when it spins. However, as the probe-magnet begins to spin CCW, the probe’s conduction electrons begin to experience radially inward pointing magnetic forces in opposition to the battery’s emf. This throttles back the CCW radial acceleration of the probe-magnet assembly. When the radial acceleration attenuates to zero, the motor has reached its maximum angular speed.
If the magnet is non-conducting, then within the probe the magnet engenders a radially inward-pointing electric field as it spins. The attendant electric forces on probe electrons cancel the Lorentz magnetic forces associated with the magnet’s rotation, leaving the battery’s emf unopposed in the probe. However, the magnet’s spin-induced E field is conservative and it engenders a CCW emf in the return wire-shaft portion of the circuit. This CCW emf opposes the battery emf and again throttles the angular acceleration back until the device reaches a constant angular speed.
In both conducting and non-conducting magnet cases, then, a self-governing mechanism limits the angular speed attained by the motor. In the conducting magnet case, the back emf is a consequence of spin-associated magnetic forces acting on probe conduction electrons. In the non-conducting magnet case, these magnetic forces are canceled by electric forces attributable to the spinning magnet’s electric field. The eventual nulling of the battery’s CW emf is caused by the spinning magnet’s conservative E field, which circulates CCW in the return wire-shaft portion of the circuit.