On the Dynamics of a Spinning, Disc-shaped Magnet
G.R.Dixon, 3/10/04
G.R.Dixon, 3/10/04
Fig. 1, copied from a previous article, shows a connecting wire/load assembly at rest in the electric field of a spinning, disc-shaped permanent magnet. This spin-induced electric field has a radial, outward-pointing component above and below the magnet (when the magnet’s spin is CW, viewed from above). Guala-Valverde et al have measured potential drops across the load, despite the fact that there is theoretically no potential rise across the return wire (Wire A in the diagram). This raises the interesting question of whether the device has a net energy gain. Energy conservation of course suggests that this cannot be the case.
Figure 1
Spinning Magnet and Load
Let I = Ne/sec be the current, where e is the electronic charge magnitude (1.6E-19 coul). The power dissipated in the load is:
. (1)
Now although there is no emf rise over Wire A, from shaft to peripheral ring, a conduction electron must have its kinetic energy increased when passing from the shaft out to the spinning ring. The rate at which kinetic energy is created is:
, (2)
where R is the ring’s radius and
w is its angular rate. Under the best conditions energy conservation requires that Pload = PKE. That is,
(3)
or
. (4)
PKE is provided by the drive shaft. That is, when a connecting wire (with nonzero load) closes the circuit, "drag" develops on the spinning magnet/ring. In order for
w to remain constant, the shaft must counteract this drag with an appropriate torque:
, (5)
or
. (6)