Randall posted this site on his blag, some time ago and I'd like to analyze what it says using a Maxwell's equations. I hope this hasn't already been done. Prove me wrong if I am, please.

Figures 1, 2 and 3

I think [imath]\vec{B}[/imath] should be changed with [imath]\vec{H}[/imath], since we are talking about electric and magnetic fields in matter. Anyway:

[math]\vec{\nabla}\times \vec{H} = \vec{J_f} + \frac{\partial D}{\partial t} \Leftrightarrow \int_{\gamma}\vec{H}\cdot d\vec{s} = \vec{I}_{enc} + \frac{\partial \Phi_{\vec{D}}}{\partial t}[/math]

We take a loop in the middle of our "toroidal inductor" for [imath]\gamma[/imath] and we get [imath]I_{enc} = NI[/imath] where [imath]I[/imath] is the electric current in the wire. We see that [imath]\vec{H} \neq 0[/imath], so a magnetic field is induced in the rod (i would take another material instead of iron, because it is ferromagnetic and this could complicate things, I think...)

Figure 4

The [imath]\vec{A}[/imath]-field is defined as: [math]\vec{A}(\vec{r}) = \frac{\mu_0}{4\pi}\int_{R^3}{\frac{\vec{J}(\vec{r'})}{|\vec{r} - \vec{r'}|}d\tau'}[/math]

The consequence is that it doesn't depend upon the presence of a magnetic field, but it is the electric current to cause it. What the author of the site writes should be false...

Figure 5 and 6

Maxwell: [math]\epsilon = -\frac{\partial \Phi_{\vec{B}}}{\partial t}[/math] where [imath]\epsilon[/imath] is the electromotrice force. If we have a steady current, then [imath]V_{out} = 0[/imath], beacuse [imath]\vec{B} = const.[/imath]. The situation illustrated in those two figures is true if we have a current that changes over time.

Figure 7

If we have current in the "secondary" wire we are in a situation very similar to the one of figures 1, 2 and 3, and the same rules applies.

Figure 8

As I have already said, there is no [imath]\vec{A}[/imath]-field there. If [imath]V_{in}[/imath] changes over time we will have an inducted electric field. Re-using the equation for the first 3 figures and supposing there is no other dielectric medium than the coils and wires ([imath]\Rightarrow \Phi_{\vec{D}} =\epsilon_0 \Phi_{\vec{E}}[/imath]): [math]\int_{\gamma}\vec{H}\cdot d\vec{s} = \vec{I}_{enc} + \frac{\partial \Phi_{\vec{D}}}{\partial t} = \epsilon_0 \frac{\partial \Phi_{\vec{E}}}{\partial t}[/math]

[imath]\epsilon_0 \approx 8.85\ \times\ 10^{-12} C^2N^{-1}m^{2}[/imath], so obviously, if we take a perfect simmetry, [imath]V_{out}[/imath] should be about [imath]10^{-11}[/imath] times [imath]V_in[/imath]. If [imath]V_in[/imath] is not really big, then [imath]V_{out}[/imath] will be very close to 0.

Figure 9

I think there would be electric current in the wire. If we take [imath]\gamma_1 =[/imath]a circle enclosing the coil and touching the beginning and the end of the wire, but not following it, and [imath]\gamma_2[/imath] a circle like [imath]\gamma_1 =[/imath], enclosing the coil and touching the extremes of the wire AND following it all around, we would have:[math]\int_{\gamma_1}\vec{E}\cdot d\vec{s} \approx \int_{\gamma_2}\vec{E}\cdot d\vec{s}[/math]

From symmetry and substracting the part of integral that are perfectly equal we can see that there is an electric field along the wire, that is to say an electromotrice force (until the condensator plates are charged, neutralizing the electric field).

Figure 10

A simple consequence of figure 7.

Figure 11 and 12

The magnetic field is quite different from the electric field, and the inducted magnetic field is different from both magnetic and electric field (it's complicated, I have not understood it really well yet...)

Figure 13

IDK, probably to put some ferromagnetic (or even diamagnetic, maybe) material would produce an inducted magnetic field opposite to the one induced by the electric current, reducing the intensity of the total field...

Figure 14

I think it should be true... More turns = more flux of magnetic field => more induced current (?)

Figure 15

This case is extremely similar to figure 9, only we put a wire (the "core") in a place instead of another. There will be electric field inside this wire, but wouldn't be easier to put a potential difference at the extremes of this new element?

I hope somebody can help me clarifying the point I'm not sure about (e.g.: is the previous sentence correct?) and correct my errors.

## Electronics for Alien Minds

**Moderators:** gmalivuk, Moderators General, Prelates

### Electronics for Alien Minds

"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."

- wbeaty
**Posts:**55**Joined:**Sun Apr 12, 2009 1:54 am UTC**Location:**Bagley Hall basement, futzing with kilowatt VHF pulse amplifiers (UW Seattle campus))-
**Contact:**

### Re: Electronics for Alien Minds

Cool!

Remember, B is the curl of A by definition.

Other good stuff:

Twenty Three Years:

The Acceptance of Maxwell's Theory

JC Rautio, MICROWAVE JOURNAL 50th commemorative

http://www.sonnetsoftware.com/support/d ... ations.pdf

WP and hyperphysics have nice descrs http://en.wikipedia.org/wiki/Magnetic_potential

http://hyperphysics.phy-astr.gsu.edu/hb ... agvec.html

The "Hertz-Heaviside" equations

http://ieeexplore.ieee.org/xpls/abs_all ... er=4638068

http://ieeexplore.ieee.org/stamp/stamp. ... r=04638068

PS

Also, what do you get when you div-grad-curl on a "psychic energy field?" Spin a Tibetan Prayer Wheel at 3600RPM, look for anomalous 60Hz signals.

The opposite of gravity is comedy, suggesting that GR has Comedic Potential not yet fully explored.

Two four-vectors walk into a bar...

From WP article:

...a depiction of the A field around a loop of B flux (as would be produced in a toroidal inductor) is qualitatively the same as the B field around a loop of current. The figure below is an artist's depiction of the A field. The thicker lines indicate paths of higher average intensity (shorter paths have higher intensity so that the path integral is the same). The lines are just drawn to look good and impart general look of the A field.

Remember, B is the curl of A by definition.

Other good stuff:

Twenty Three Years:

The Acceptance of Maxwell's Theory

JC Rautio, MICROWAVE JOURNAL 50th commemorative

http://www.sonnetsoftware.com/support/d ... ations.pdf

WP and hyperphysics have nice descrs http://en.wikipedia.org/wiki/Magnetic_potential

http://hyperphysics.phy-astr.gsu.edu/hb ... agvec.html

The "Hertz-Heaviside" equations

http://ieeexplore.ieee.org/xpls/abs_all ... er=4638068

http://ieeexplore.ieee.org/stamp/stamp. ... r=04638068

PS

Also, what do you get when you div-grad-curl on a "psychic energy field?" Spin a Tibetan Prayer Wheel at 3600RPM, look for anomalous 60Hz signals.

The opposite of gravity is comedy, suggesting that GR has Comedic Potential not yet fully explored.

Two four-vectors walk into a bar...

From WP article:

...a depiction of the A field around a loop of B flux (as would be produced in a toroidal inductor) is qualitatively the same as the B field around a loop of current. The figure below is an artist's depiction of the A field. The thicker lines indicate paths of higher average intensity (shorter paths have higher intensity so that the path integral is the same). The lines are just drawn to look good and impart general look of the A field.

((((((((((((((( ( (o) ) )))))))))))))))

William Beaty . . .Science Hobbyist page

http://amasci.com . . billb o eskimocom

William Beaty . . .Science Hobbyist page

http://amasci.com . . billb o eskimocom

### Re: Electronics for Alien Minds

I will contest that the last figure is not an electro-electret. It is a magneto-electret. It just happens to be driven by an electro-magnet, but it wouldn't need to, a spinning permanent magnet would work as well.

- wbeaty
**Posts:**55**Joined:**Sun Apr 12, 2009 1:54 am UTC**Location:**Bagley Hall basement, futzing with kilowatt VHF pulse amplifiers (UW Seattle campus))-
**Contact:**

### Re: Electronics for Alien Minds

Weird A-field trivia: Carver Mead wrote a 'crackpot physics' book where A-fields play a significant role:

COLLECTIVE ELECTRODYNAMICS: QUANTUM FOUNDATIONS OF ELECTROMAGNETISM, Mead 2002

http://www.pnas.org/content/94/12/6013.full

http://www.math.umb.edu/~sp/mead.pdf

http://www.amazon.com/Collective-Electr ... 0262632608 [note reviews!]

COLLECTIVE ELECTRODYNAMICS: QUANTUM FOUNDATIONS OF ELECTROMAGNETISM, Mead 2002

http://www.pnas.org/content/94/12/6013.full

http://www.math.umb.edu/~sp/mead.pdf

http://www.amazon.com/Collective-Electr ... 0262632608 [note reviews!]

((((((((((((((( ( (o) ) )))))))))))))))

William Beaty . . .Science Hobbyist page

http://amasci.com . . billb o eskimocom

William Beaty . . .Science Hobbyist page

http://amasci.com . . billb o eskimocom

### Re: Electronics for Alien Minds

wbeaty wrote:Weird A-field trivia: Carver Mead wrote a 'crackpot physics' book where A-fields play a significant role:

COLLECTIVE ELECTRODYNAMICS: QUANTUM FOUNDATIONS OF ELECTROMAGNETISM, Mead 2002

http://www.pnas.org/content/94/12/6013.full

http://www.math.umb.edu/~sp/mead.pdf

http://www.amazon.com/Collective-Electr ... 0262632608 [note reviews!]

I think I'll wait a semester before adventuring in such a topic... I don't have any knowledge of quantum mechanics yet

"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."

### Re: Electronics for Alien Minds

wbeaty wrote:Weird A-field trivia: Carver Mead wrote a 'crackpot physics' book where A-fields play a significant role:

COLLECTIVE ELECTRODYNAMICS: QUANTUM FOUNDATIONS OF ELECTROMAGNETISM, Mead 2002

http://www.pnas.org/content/94/12/6013.full

http://www.math.umb.edu/~sp/mead.pdf

http://www.amazon.com/Collective-Electr ... 0262632608 [note reviews!]

I just checked out this book from my library, and started both my intermediate level EM and QM courses this semester, as such, I'm not really in a position to gauge the accuracy of the the book. Has anyone else read/reviewed the material in it? Is this a good idea to apply some of the ideas in my regular work?

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