Permanent magnet motor

[lumen]

Apples and oranges.  The keeper is a highly permeable block that changes the field concentration.  It dramatically changes the magnetic path length.   Energizing or deenergizing a magnet does not change the magnetic path.  It changes the magnetic excitation.

The keeper is closing the magnetic loop to retain the loop inside the magnet. It's the same as bending the magnet ends to make a closed loop so the external field is reduced to near zero.

There is a world of difference between zero and some.  The more permeable the material the less the leakage.  But there is always leakage.  If you go get an iron pipe and energize a wire running through it, yes the leakage will be low, but it will still be there.  You have been wondering if you can get a PM to produce the same field pattern as a copper wire.  The answer is yes.  The material having a higher permeability than copper means that the model is of a powered copper wire inside a core of that permeability.

I agree there is some leakage, but the more circular and consistent the field is, the less leakage exists.

Yes, and so what?  The first requirement is that you can get the same field shape.  The second is retaining the shape.  If your objection is that a field will concentrate in highly permeable material, that has nothing to do with being able to magnetize in a circular pattern or not per se.  Since you would like most of the field to remain outside the core, then that is a matter of materials choice.  You could for example sinter a core of powdered ferrite magnet or ceramic magnet material so as to greatly reduce the permeability, and thereby greatly increase the proportion of the field that extends beyond the core circumference.

That entire magnetic weld tester is dependent on the flaws to cause more field leakage, that's how it works. Without the flaws there is near zero leakage.
The permeability of the core changes nothing, a ring of weak magnets leaks the same as a ring of strong magnets.

You are going to need to explain why you think that would be so.  I don't see where such a conclusion follows at all. 

A motor operates by repeatedly changing the location of the potential energy minimum.  Moving the PE minimum location when the system is at any location other than the new minimum takes work.  Some of that work, and in a well-designed motor almost all of that work, conveys to the motor mechanical output.

If all motors worked on that principal then there would not be any reason to pursue the circular field.
However that is not the case in a Faraday motor using only a single field of uniform strength.
A single conductors circular field will direct more flux from the uniform field to one side of the conductor without itself interacting with the uniform field. This imbalance is what pushes the conductor in a continuous circular path in the uniform field as the field tries to maintain uniform spacing.

If a magnet could be made to produce the field of a conductor with current, it would be a simple matter to replace the conductor and have a fully permanent magnet motor.

[MarkE]

The keeper is closing the magnetic loop to retain the loop inside the magnet. It's the same as bending the magnet ends to make a closed loop so the external field is reduced to near zero.

You are saying almost the same thing.  The small but important distinction is that it keeps most, not all of the flux within the magnet and the keeper.

I agree there is some leakage, but the more circular and consistent the field is, the less leakage exists.That entire magnetic weld tester is dependent on the flaws to cause more field leakage, that's how it works. Without the flaws there is near zero leakage.

I agree.  But the point is that the field can be shaped the way that you want, which is Step 1.  Step 2. is to get the field to persist in that pattern with the power turned off.  And Step 3. is to get a useful amount of the flux to distribute outside the core.  Step 1 has been shown as in the inspection methods.  Steps 2 and 3 are matters of material selection and coming up with a strong enough magnetizing field.

The permeability of the core changes nothing, a ring of weak magnets leaks the same as a ring of strong magnets. 

Oh, no that is just not true.  Go get two toroids, one made of a power ferrite with a uR of 2000 or so, and another made of powdered iron with a uR of 50 excite them well below the saturation of the ferrite and compare the leakage.

If all motors worked on that principal then there would not be any reason to pursue the circular field.

I contend that principle is fundamental to all electromechanical actuator designs, not just motors.  You are of course free to argue differently.

However that is not the case in a Faraday motor using only a single field of uniform strength.
A single conductors circular field will direct more flux from the uniform field to one side of the conductor without itself interacting with the uniform field. This imbalance is what pushes the conductor in a continuous circular path in the uniform field as the field tries to maintain uniform spacing.

I contend that if you do the math, you will find that as long as the motor runs, the conductor never reaches a state of minimum potential but does constantly move towards it.  The position of minimum potential constantly moves with the conductor. 

If a magnet could be made to produce the field of a conductor with current, it would be a simple matter to replace the conductor and have a fully permanent magnet motor.

That I completely disagree with.  Perhaps this will help:  In order to sustain the current through the conductor, over and above the I*R voltage drop, the power source has to overcome the BEMF.  The useful power conveyed through the motor is limited to the product of the torque generating current and the BEMF voltage.  So, if you make a permanent magnet emulate the field from a wire, in this particular case a straight wire, then you eliminate the I²R losses of the motor, but do nothing to replace the torque current * BEMF product.  That's what PMDC motors do: Eliminate the copper losses associated with creating a magnetic field.  The power that is conveyed through the motor still has to be supplied from the outside, PMs or no PMs.

[lumen]

I contend that if you do the math, you will find that as long as the motor runs, the conductor never reaches a state of minimum potential but does constantly move towards it.  The position of minimum potential constantly moves with the conductor. 

How is that possible in a uniform field?
The conductor cannot be seeking a minimum potential because there is none.
If you look closely at the principals of a Faraday motor or Homopolar motor or generator, you will see that these all use a uniform field.
A big misconception is that a generator or motor requires changing flux density to operate.
In fact all magnetically induced generators work only by a conductor cutting flux lines, changing the flux density is only an easy way to achieve it.

[guest1289]

Here Is  A  Slightly  Strange  Solution  To  Making  A  Donut-Shaped-Magnet,   With  The  Magnetic-Field  Running  Around  The Circle / Donut

Make the  Donut  as an empty shell,  and make the shell out of a mesh,  each individual piece of the mesh could be  a  'small'  'Stick-Shaped-Magnet'( small longish  bar-magnet ).   
     For example,  four  small  'Stick-Shaped-Magnets'  make up one  Diamond-shape  of the mesh.

The Reason I Think The Above May Be A Solution  :
    When I read about your  'Welding-Fault-Tester',  it made me wonder  if  the  above   'Donut-Shaped-Magnet' ( made out of the  mesh ),   would  leak  out  some of  it's   magnetic-field   along it's  surface,  because of the principles of the  'Welding-Fault-Tester'.

[lumen]

Here Is  A  Slightly  Strange  Solution  To  Making  A  Donut-Shaped-Magnet,   With  The  Magnetic-Field  Running  Around  The Circle / Donut

Make the  Donut  as an empty shell,  and make the shell out of a mesh,  each individual piece of the mesh could be  a  'small'  'Stick-Shaped-Magnet'( small longish  bar-magnet ).   
     For example,  four  small  'Stick-Shaped-Magnets'  make up one  Diamond-shape  of the mesh.

The Reason I Think The Above May Be A Solution  :
    When I read about your  'Welding-Fault-Tester',  it made me wonder  if  the  above   'Donut-Shaped-Magnet' ( made out of the  mesh ),   would  leak  out  some of  it's   magnetic-field   along it's  surface,  because of the principles of the  'Welding-Fault-Tester'.

It's not hard to get some or even a large amount of field outside of the circular loop by spacing the magnets, the problem is that in each space that allows the field to exit, it also allows a field to enter.

That does not occur in the circular field produced from current flow and that is why it is unique and cannot be generated with magnets.
Each gap has an IN and an OUT when constructed with magnets, but only the OUT exists in the field of a conductor.
It will take a much more complicated approach to achieve if it's ever possible, some new materials and research maybe.