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Vector potential

  1. Aug 16, 2007 #1
    i am having trouble visualiszing what vector potential A means physically. I understand that if you take the curl of it it give you the magnetic field B. I was wondering if anybody could also direct me to a website or show me a proof of how the electric field E is equal to the partial derivative of A with respect to time minus the grad of the scalar potential. I have no clue where to find that proof and neither do i possess a text book that has the proof in it.
     
  2. jcsd
  3. Aug 16, 2007 #2

    Pythagorean

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    I still don't understand the physical significance of A. My teacher told me there wasn't really one... it was just a mathematical relationship. Anyway, it seems to be in the same direction the E field that gets induced by the B field (which may or may not be induced by an original field, E1)


    how E = dA/dt:

    use Maxwell's Equations, maybe the divergence theorem or one of those other integral forms.... I'm having deja vu:

    http://en.wikipedia.org/wiki/Maxwell's_equations
     
  4. Aug 16, 2007 #3
    Your teacher is right on this one. The A-potential is introduced in the EM formalism to write the theory in a symmetrical way. It makes the step towards field theory more logic in the sense that the A field plays the role of the EM gauge field. Also, this potential is used to impose gauge-conditions to set the remaining degree of freedom that arises due to the definition of the A-field.

    More here : http://en.wikipedia.org/wiki/Magnetic_potential

    marlon

    edit : you should also wonder about the question why they call the A field a POTENTIAL ! :wink: (hint : look at the definition of the scalar potential)
     
    Last edited: Aug 16, 2007
  5. Aug 16, 2007 #4
    so can i think of A as being a field who's rate of rotation equals the magnetic field and who's field velocity is equal to the electrical field.
     
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