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Can anyone give me an intuition of why the magnetic vector potential $A$ is sometimes interpreted as the electromagnetic momentum ?

I don't know analytical mechanics, just classical electromagnetism

Keith
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  • Who refers to the vector potential as momentum? That's nonsense, AFAIK. – ACuriousMind Nov 05 '14 at 03:07
  • Yes I'm wrong. It's sometimes interpreted as electromagnetic momentum Edited – Keith Nov 05 '14 at 03:08
  • See http://physics.stackexchange.com/questions/53020/how-to-interpret-the-magnetic-vector-potential – Cheeku Nov 05 '14 at 03:15
  • I already check that one. The problem is that in the solution they show some things that I don't understand, like "canonical momentum ". I search for a more elementary answer – Keith Nov 05 '14 at 03:18
  • You might find this helpful: "Potential Momentum, Gauge Theory, and Electromagnetism in Introductory Physics" http://arxiv.org/abs/physics/9803023 – Alfred Centauri Nov 05 '14 at 03:36
  • @AlfredCentauri I think it's still to advanced for me – Keith Nov 05 '14 at 03:38

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In Lagrangian mechanics, one usually introduces the "generalized momentum" as $$ p_{\phi_i}:=\frac{\partial L}{\partial \phi_i} $$where $L$ is the Lagrangian depending on a bunch of generalized coordinates $\phi_1\dots\phi_n$. If you introduce electromagnetic forces, you can derive, that the Lagrangian in the presence of an electromagnetic field has a form like $$ L=\frac{m}{2}\left(\vec{p}-\frac{q}{c}\vec{A}\right)^2+q\Phi $$ where $A$ is your vector potential and $\Phi$ your scalar potential, therefore your generalized momentum will be shifted by $A$, i.e. if you write down the respective Newton equation, instead of $\dot{p}$ you will have this shifted by $A$.

The physical meaning behind this formal stuff is, that the electromagnetic field actually carries a momentum, which can be translated into a mechanical momentum. For example, I remember an experiment, where you put two spherical shells into a magnetic field and then turn the field off, the shells will get an angular momentum (I searched for it, didnt find it yet, will update if found).

Daniel
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    Ok. Thanks for the answer. So that means that the total momentum of any particle interacting with a magnetic field is less by a factor of $A$. Why is this ? Any intuition , if the particle is on magnetostatic field is different from a changing current in time. Does this affect the energy of the particle By some other factor of $A$? – Keith Nov 05 '14 at 03:29