But what is the magnetic vector potential?

r-serra commented 2 years ago

About the author

I'm an assistant professor in the Netherlands. My area of expertise is called Electromagnetic Compatibility (or how to make your electronics work together without interfering with each other).

I'm also a passionate teacher and increasingly interested in gaining expertise to produce good educational videos. I'm a big fan of 3B1B (and many good channels out there).

I do not have the time, the knowledge or the drive to invest in learning how to make good animations, or video editing.

Quick Summary

I'd like to talk about the magnetic vector potential. This is a key physical quantity to solve many types of electromagnetic radiation problems. However, almost all explanations fail to deliver a good intuition on its physical meaning, or even on its mathematical relevance. I often feel deeply frustrated when I hear teachers introduce this vector potential as merely "an aid to calculate magnetic fields". It is also frustrating to see how students are more able to accept and assign a physical intuition to the electric scalar potential (its cousin), but not to the vector potential.

Target medium

My (ideal) collaborator is a good writer, has mathematical plotting skills, can maybe narrate (I have a very heavy accent in English) and can edit videos.

More details

The story that I want to share would explain the mathematical benefits of using magnetic vector potentials, but also provide a physical meaning to them, which will illuminate the mathematics behind. For instance, I've had an immense feeling of (intellectual) joy after watching this video.

I know I can provide a similar (mutatis mutandi) feeling explaining the vector potential.

One (to me) fascinating aspect of this explanation is that it is coming from James Clerk Maxwell himself! The story behind this explanation has many historical aspects, battles, debates, etc.

I am sure that I can even try to build a mechanism which could illustrate the concept, not only animations and plots. So, more on the Steve Mould style.

Finally, there is a nice takeaway, but probably more pertinent to electrical engineers and physicists than to the general audience, but I'd like to show how ignoring the vector potential causes industry losses of billions of dollars per year!

Contact details

React to this issue?

Additional context

Knowledge_clip_on_a_visualization_of_the_magnetic_vector_potential.pdf

FAUM commented 2 years ago

Not an animator or anyone who can contribute to this in the way that's sought. But I have to say -- excellent video topic! Excited to see how this develops!

r-serra commented 2 years ago

Not an animator or anyone who can contribute to this in the way that's sought. But I have to say -- excellent video topic! Excited to see how this develops!

Thanks for your kind words. Good luck with fractals as well!

3b1b commented 2 years ago

Hi, I'd be interested in hearing more about what you have in mind. Do you have any links to talks/articles you've written describing the kind of "physical meaning" you have in mind? Are there any particular motivating examples you'd use to introduce a student to the magnetic potential? What about any sketches for the visuals you'd aim for?

r-serra commented 2 years ago

Hi, I'd be interested in hearing more about what you have in mind. Do you have any links to talks/articles you've written describing the kind of "physical meaning" you have in mind? Are there any particular motivating examples you'd use to introduce a student to the magnetic potential? What about any sketches for the visuals you'd aim for?

Hi Grant! Thank you so much for being interested in my proposal! Apologies for this late reply, but I've been very busy the last days. Moreover, I did not have anything written which could add more context to my proposal... Today I found time and put some ideas in a document. I have just attached it to the description above and also here: Knowledge_clip_on_a_visualization_of_the_magnetic_vector_potential.pdf

To give some quick answers to your questions:

The physical meaning of the vector potential is that of the velocity field of a series of hypothesized spheres whose movements propagate perturbations from electric currents through space. More in the attached document.
My motivation to students (before thinking of the way described in the document) was purely instrumental. The vector potential is that vector which helps us simplify the in-homogeneous Helmholtz equation. An instrument, or an aid. Similar to the concept of instant center of rotation, for instance. This fictitious center of rotation is not really a center of rotation. But if we assume it as one, which works only instantaneously, some simplifications are possible to solve certain problems...
Sketches and visuals is what is hard for me. In the document there is a snapshot of a diagram taken from Maxwell's paper. The paper which gave me the idea. I could try to draw something , but it's definitely not a skill I master. If you're still interested and find that the document is not clear enough, I could attempt some graphics...

Looking forward to hearing from you!

3b1b commented 2 years ago

Hi Ramiro, thank you for taking the time to write this up, and my apologies for being so late in replying to it!

I have some more questions, but it might be most efficient to hop on a brief zoom call to ask in person. Do you happen to have any free time on Monday/Wednesday? (I'm on pacific coast time).

mjluser1 commented 2 years ago

@r-serra @3b1b Hi, I have some figures and an Einstein's equation that would be helpful. The images are visualizations of the magnetic vector potential using Maxwell's later work. His "Theory of Light" (Treatise, Vol. 2, Chap. XX) forms a light wave from two opposing circularly polarized waves in the A field of the magnetic vector potential.

I have uploaded the images as part of a brief excerpt from a short ebook draft. As it explains, there are two factoring solutions of Einstein's 1905 summary equation for the electromagnetic interval, which I discovered is the governing equation for Maxwell's A field.

If this interests you, would you consider having a third collaborator? I deeply appreciate Grant's 3b1b videos, as well as his videos and articles for Khan Academy. I would like to work with both of you on this project.

Lindeman-MassFromLight-DRAFTV6-excerpt_for_3B1B.pdf
I included the ebook's title page, table of contents, and the current full list of references to help establish some context for the two chapters.

leios / SoME_Topics