Your reference is noted, but I have some concerns about it.  Clearly they are trying to explain a TT Brown type drive system, but I will argue strongly against the magnetic or electric fields having ANY moment of inertia, especially in the opposite direction of motion.  This is clearly just an attempt to balance the equation. Second, the last image in your reference appears to show the magnetic field passing through the source of electric field, which it does not.  So I can only agree with the first 2 animated bits of your reference.
With regard to the biot savart law, clearly it applies to currents in a wire and can be applied to wires of some width.
  A major problem then arises in unipolar generators that have rotors saturated with current.  The application of those equations falls apart because the current ends up having an infinite width.  You should recognize that infinite values destroy standard mathematics and new mathematical models must then be developed.  I've attached below a hand written analysis done for me personally by the Head of Forward Development at Delco-Remy America in Anderson Indiana where I gave a technical presentation in 2003.  In it you will find his textbook analysis to be flawless, but I note the same thing (in colored text) as here.  The unipolar generator (when saturated with current) is the only stable way to continuously violate historical mathematics, and further; it exists in nature as hurricanes, tornadoes, galaxies, the Sun, the Earth, and the atom to name a few examples.  Please look to see if you can find another way to explain the stability of tornadoes, they are quite real as is the violation of Newtonian "Law" on a swingset.
-BWS

The only thing I can see wrong with this formula is the sign is wrong. This is because the current was not generated in the disk but in the wire connected to the brushes. The disk is not cutting any field because it spins with the magnet.
The magnetic lines of force are generated by the electron spin in the atoms of the magnet. The atoms at the outer rim of the magnet are not just spinning on their axis but moving in a circular path. Why would it not drag it's force lines around with it? Answer: It does!

@lumen

Indeed, you do have a wonderful quality. You are wonderfully persistant!

BEP

@all:

Glue a dime in the center of a quarter.  On the dime place a black dot at the 12, 3, 6, and 9 O'clock position.  The dime is the electron and the quarter is the magnet.  Now rotate this quarter any way you like and you will see that the black dots move with the magnet. If this doesn't convince you, then let's do another test.

Imagine the quarter is stationary with the dime spinning at 100,000 rpm around its axis.  Now rotate the quarter while the dime is spinning.  If the electron's spin is independent of the quarter, then if the quarter is moving at 500 rpm, then the dime is moving at 100,500 rpm, thus the field or flux is moving with the magnet.  If the electron's spin is not independent on the quarter or magnet, then the dime or electron would be spinning at 999,500 rpm relative to the quarter or magnet, thus the field or flux is moving with the magnet.  If the quarter matched the speed of the electrons rotation, then the field would be stationary when the magnet is moving.  So, as you can see, the field can only be stationary if the electrons speed is not independent on the the spin of the quarter and the magnet is rotating at the same speed of the electron.  If the speed of rotation of the electron is independent from the speed of rotation of the magnet, then the speed of the magnet can never reach the speed of the electron in order for the field to be stationary.

I think most of us will agree that the speed of rotation of the electron is independent from the magnet (wouldn't surprise me if most disagree....LOL).  As you can see with the quarter and dime, the field or flux can never be stationary when the magnet is rotating on it's axis if the electron's speed is independent of the magnet.

@BEP,  Persistence is a powerful force.  A persistent drop of water can carve out deep valleys over thousands or millions of years.  If we didn't believe as strongly as we do, then we wouldn't be as persistent.

Quote from: BWS on May 14, 2009, 08:02:01 AM
Note that you can never violate Newton with a coil, but if you induce voltage in wire segments you are home free.  I can explain this further if requested.

Could you please explain for me.  As you may have noticed, my imagination runs wild.

Quote from: BWS on May 14, 2009, 08:02:01 AM
The force acting on the induced electron does not act on the source of the magnetic field.
-BWS
-BWS

The force being the magnetic field and the source of the magnetic field being the electron?

That is a very clever statement.  At first I thought that statement was contradictory to accepted physics, but then after analyzing the statement, it isn't contradictory.  Your statement is different from saying the induced electron has a magnetic field that opposes the force that induced it. 

I think the electrons do undergo an opposing force and it is the orbital momentum of the electrons that overcomes this force to give us torque (this is another reason why the field or flux can't be stationary when the magnet is spinning on it's axis, cause the electrons has an axial and orbital spin or intrinsic 1/2 spin meaning the electron has to turn 720 degrees before seeing the same face again).  No opposing force, then no torque.  I have to think about your statement more. 

I'll allow broli to mention how having many turns of the wire may overcome this problem in the classical homopolar generator.  Although he's already posted while I'm still editing this post (A bad habit of mine).

I apologize for being so technical and persistent.

Thanks BWS,

GB