In their rebuttal to the critics of their original paper, "Further
Considerations on Electromagnetic Potentials in the Quantum Theory",
Physical Review, August 15, 1961, Aharonov and Bohm state that a
moving electron will have a back-reaction on to a source of A
(magnetic vector potential). Unfortunately they did not further
explain this back-reaction. After posting my message (MEG_builders
message #1204, Sep 11, 2003) about the convective derivative, how
the velocity of charge is affected by it's motion through a gradient
of A, I wanted to observe some change in the magnetic field of an
output coil which may be caused by such a condition. I built a
transformer on a nanocrystalline core with small "sense" coils at
the base of the output coil. Two sense coils are on the outside of
the leg of the core, two others are in the interior space of the
core.

See the bitmap image, "ACoreTst1.bmp".
Go to "Files" then go to the folder "MESSAGE ATTACHMENTS", go
to the folder "Results from a new A-Theory", and open
"AcoreTst1.bmp".

The basic core is a Honeywell AMCC-320, cut core (The core has
been cleanly cut into two halves. Uncut cores can be purchased
also, and will have lower reluctance because there is no gap from
the cut). Honeywell cores can be purchased from Eastern Components,
www.eastern-components.com.

Spaced from the core by 0.02-inch-thick tape, the ferrite sense
coils are placed at the side and the center of the leg of the main
core. This was to provide an indication of any differences between
the outside edge of the output coil and its center. Above the
sense coils is a sheet of 0.002-inch thick brass which acts as a
shield to any electrical field between the output coil and the sense
coils. (Typically the output coil operates at several hundred volts
peak, and coupling of that voltage into the sense coils could mask
measurements of the magnetic field.) The ends of this shield layer
are insulated from one-another to prevent it from becoming a
shorted turn which of course would kill the transformer action.

There is another layer of 0.02-inch tape over the brass shield
to reduce the capacitance between it and the output coil. The
output coil is a bifilar (two wires in parallel) winding of #23
enamel-coated magnet wire, of 23 bifilar turns per layer, with
a 0.006-inch layer of teflon tape between the winding layers.
There are a total of 13 layers for a total of 299 bifilar turns.
Then end of one bifilar wire is connected to the start of the
other wire to provide an effective total of 598 turns. At the
junction of the two wires, a capacitor can be placed to adjust
the series-resonant frequency so that different operating
frequencies can be tested (This series resonance is between the
transformed capacitance of the output coil and the leakage
inductance of the drive coil).

In the illustration, a permanent magnet is shown. Tests
were made with and without a stack of Neodymium magnets to note
any differences.

The outside sense coils are in a region where there is only
one contribution to the A-field, from the leg of the core. The
other sense coils are in the interior space of the core where
there are contributions from the top, bottom, and the leg of
the core. The magnetic-vector-potentials are additive, in
accordance with the usual vector addition (direction and
amplitude are equally important).

See the bitmap image, "AgradCor1.bmp".
Go to "Files" then go to the folder "MESSAGE ATTACHMENTS", go
to the folder "Results from a new A-Theory", and open
"AgradCor1.bmp".

The image illustrates the A-potential vectors as I visualize
them around the nanocrystalline core. This drawing was to
illustrate the static A from a permanent magnet, but it also is
true for the dA/dt when the core is used as a transformer. In the
case of the dA/dt, there are only three contributions to the A in
the interior of the core space, A from the magnet is ignored.

I had anticipated that where the A-potential was greatest, there
would be the greatest B-field reaction from the electrons moving
in the coil. Instead what I find is that the volume where the
A-potential is weakest (outside the core leg), has the greatest
B-field from the output coil. I'm cetain I'm observing the
B-field, and it is solely from the current in the output coil.
This was verified by driving the core at low frequencies where the
drive coil would magnetize the core significantly, but little
resonant current and only load current would occur in the output
coil. The jpeg, "AllSigsLowFreq.jpg", illustrates this. This
image is in the folder "Results from a new A-Theory".

Channel 1 of the oscilloscope is connected to the side-mounted
sense coil on the outside of the core leg, channel 2 is connected to
the side-mounted sense coil on the interior side of the core leg,
channel 3 is the timing clock from the drive-coil logic, and channel
4 is connected to the output coil through a 200:1 voltage divider.
There is a simple R-C filter on the sense coil outputs to linearize
their response with frequency so that the voltage indications at
different frequencies will be proportional to the magnetic field,
and not the frequency. The top trace is the clock for the drive-
coil controller and its leading-edge indicates the beginning of a
cycle. Digital logic makes each phase of the drive signal about 49%
of the period, which provides a square wave to the drive coil.
Channel 1's trace is just below the square-wave of the driver-
controller signal, and ranges from about 3.3 divisions above the
bottom of the screen to about 6.7 divisions. Thus the peak-to-peak
signal is about 3.4 divisions at 50 mV/division for an amplitude of
170 mV. Channel 2's trace ranges from just about 0.3 division above
the bottom to about 3.9 divisions at 20 mV/division for an amplitude
of 78 mV. The output voltage ranges from 2.8 divisions to 5.1
divisions at 200 volts/division for an amplitude of 460 volts. Thus
the ratio of voltages between the two sense coils is 170/78 which is
2.2 to 1. NOTE: the notation at the bottom of the screen says
800VP-P and was for a different measurement and is in error for this
measurement. The load on the output coil was 15k ohms. Also, only
one wind of the bifilar coil was used, so that resonance of the
output coil would be at a frequency much higher than the operating
frequency for this test. I didn't want resonance effects to
interfere with the transformer action.

The image, "AllSigsHiFreq.jpg", in the folder "Results from a new
A-Theory", illustrates the output coil operating in series resonance
with the drive-coil. A 500 pF capacitor and 2.2 mH inductor are in
series between the end of one bifilar wire and the start of the
other. The 2.2 mH inductor was placed to allow higher frequency
effects such as the Lenz pulse to occur more easily (less capacitive
loading of the core). Note that the channel 1 and 2 sensitivities
have been changed significantly. Channel 1's signal now ranges from
3.5 divisions to 6.5 divisions at 200 mV/division for a total
amplitude of 600 mV peak-to-peak. Channel 2's signal ranges from 0.8
divisions to 3.2 divisions for an amplitude of 240 mV. The ratio of
the two sense coils is 2.5 to 1. The output coil amplitude is now
6 divisions at 200 volts/division for a total amplitude of 1,200 volts
peak-to-peak. As noted on the screen, there is a 60k ohm load
connected to the output coil.

NOTE: the sense-coil signals are shifted (delayed) about 90
degrees (1/4 cycle) due to the R-C filters. Without the R-C filters,
the signals from the sense-coils are in phase with the output voltage,
as they should be, but then high-frequency artifacts appear stronger
than they are in reality.

The image "CoreBuildUp.jpg", in the folder "Results from a new A-
Theory", shows the built-up core. There are two drive coils in place
to try different resonance frequencies because the leakage inductance
will change based on the length of the magnetic path from the drive
coil to the output coil. The output coil being tested is on the
right-hand side of the image, where the coaxial-cable connections to
two of the sense coils can be seen. The output coil on the left has
the connections to each layer brought out so that experiments can be
performed with different total turns in its circuit.

A note about the drive circuit: it is composed of four MOSFETs in
a bridge configuration so that the full supply voltage can be applied
across the drive coil for each phase of the drive. For this test,
it's only function is to provide a variable-frequency square wave to
the drive coil to provide large values of dB/dt in the core, and
consequent large values of dA/dt outside the core. A simplified
circuit diagram can be seen in the image "TestCir1.bmp", in the
folder "Results from a new A-Theory".

The ratio of measured B-field inside the output coil is close to
the 3:1 value of the A strength ratios in my idealization. Why they
are not precisely 3:1 is probably due to the fact that I have
approximated the A values, and because A is not blocked by the core
(or any other physical matter) there are some vectorial subtractions
occurring due to vectors interfering around the output coil which
results in less than a 3:1 ratio occurring.

By the way, the addition of the permanent magnet to the core
did not change the ratio significantly and I have not made precise
measurements of its impact at this time. The difference in ratio
may have been 10%, not a lot compared to the basic ratio. The
images in this report are those with the magnet in place.

Also, there was no significant difference in signal level
between the sense-coils on the outside of the leg versus
those at the center.

To help eliminate experimental error, I built an entirely
different configuration, on an AMCC-1000 uncut core, which is
dramatically different in size from the AMCC-320. The sense-
coils are also very different in size. The effect is
repeatable as the measured ratio between outside and interior
of the core is 3.2:1 which is close to that reported here.

A symmetrically wound coil will have a reasonably uniform
magnetic field at points that are symmetrically similar. (The
field distribution in a rectangular shape is not uniform, although
at symmetric points around the center of the shape the field will
be the same.) This experiment indicates to me that the magnetic
vector potential is real, as theorized by Aharonov and Bohm, and
that we have not fully exploited it as yet.

David J.

Files:
ACoreTst1.bmp
AgradCor1.bmp
AllSigsLowFreq.jpg
AllSigsHiFreq.jpg
CoreBuildUp.jpg
TestCir1.bmp