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Magnetic Vector Potential

  1. Mar 16, 2012 #1
    1. The problem statement, all variables and given/known data

    For the magnetic field B=k/s3 z determine the magnetic vector potential A. For simplicity, assume that A does not have a component in the s direction.

    (I don't know if this is relevant but this was a follow up question to one in which I was required to find the induced current for a bar moving along a semicircular loop of wire - like a slide wire generator bent into a semicircular shape - and then the torque on the bar due to the magnetic force and then the position ∅ at which the bar comes to rest.)

    2. Relevant equations

    Curl of A = B

    Divergence of A = 0

    3. The attempt at a solution

    The z component of the curl of A in cylindrical coordinates is:
    1/s[d(sA)/ds - d(As)/d∅]

    The B field we are considering has only a z component so the s and components of the curl of A can be disregarded. Also, we are told in the problem that As = 0 so the only surviving term, equal to B, is:

    1/s d(A)/ds = k/s3

    Separating the variables:

    ∫ d(sA) = ∫ (k/s2) ds

    After integration, we get:

    A = -k/s2 + C/s

    Where C is the integration constant.

    This is as far as I got....I'm not sure how how to find out what C is. Any tips would be appreciated!
     
  2. jcsd
  3. Mar 16, 2012 #2

    tiny-tim

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    Science Advisor
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    hi beth92! :smile:

    vector potential is like scalar potential …

    only the potential difference matters, so you can add any constant vector you like! :tongue2:

    i'd add 0 o:)
     
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