The A Field?

1. Nov 1, 2006

Jdo300

The "A" Field?

Hello All,

A while ago, I had a chance to read this research paper that was trying to explain how the "Marinov Motor" works. In the paper, they explain that it does not use regular induction through magnetic B fields, but instead makes use of the "A" field. I don't remember reading anything about this field in my physics book and was wondering if anyone could point me in the right direction to some good introductory info about it. I heard it has to do with magnetic potential or something. In case you are interested, I also attached the file I was looking over.

Thanks,
Jason O

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2. Nov 1, 2006

quasar987

It is the magnetic vector potential. (One form of one of) Hemlhotz's theorem says that any divergenceless vector field $\vec{B}$ can be written as the curl of of a vector field:

$$\vec{B}=\nabla \times \vec{A}$$

Note that just as the electric potential or the potential energy function in mechanics, the potential vector $\vec{A}$ is not unique but rather for any $\vec{A}$ such that
$\vec{B}=\nabla \times \vec{A}$, $\vec{A}+\nabla\lambda$ where $\lambda$ is any (properly bahaved) scalar function is another vector potential for $\vec{B}$.

Additionally (though this information might be superfluous at this point, it is very important), according to (another version of another) Helmhotz theorem, any vector field can be written as a function of its curl and its divergence only. Since we only need that the curl of A be B, we can litrally choose any value we want for the divergence of A.

Last edited: Nov 1, 2006
3. Nov 1, 2006

cesiumfrog

This paper doesn't seem to refer to what google calls the http://www.electricstuff.co.uk/bbmotor.html" [Broken]. The latter does not really depend on fields; a current selectively heats and deforms ball bearings so that they (through frictional forces) apply an acceleration.

Last edited by a moderator: May 2, 2017
4. Nov 2, 2006

Jdo300

That is not the Marinov motor I am looking into. Here is another document referencing it:

http://redshift.vif.com/JournalFiles/Pre2001/V05NO3PDF/v05n3phi.pdf

@quasar987,

Thanks for the info. What physical significance does the A field have? What physical entities does it react with? Or is it just some sort of mathematical abstraction?

Thanks,
Jason O

Last edited by a moderator: May 2, 2017
5. Nov 2, 2006

quasar987

I quote Feynman:

From lecture 15 chapter 5 of volume 2.