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Scalar and vector potentials and magnetic monopoles

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Write down expressions oer E and B fields in terms of [tex]\varphi[/tex] and [tex]\bar{A}[/tex]. Demonstrate that this definition of B is consistent with the non-existence of magnetic monopoles.

    2. Relevant equations



    3. The attempt at a solution

    The first part of the question is easy. i.e. bookwork
    [tex]B = \nabla \times \bar{A}[/tex]
    [tex]E = \nabla\varphi - \frac{\partial{A}}{\partial t}\[/tex]

    I dont know how to approach the second part of the question though
     
    Last edited: Apr 16, 2010
  2. jcsd
  3. Apr 16, 2010 #2

    tiny-tim

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    Hi peterjaybee! :smile:

    Hint: there is electric charge, but (if there are no magnetic monopoles) there's no magnetic charge (ie, you can't have a particle or an object with overall magnetic charge) … so how does electric charge come out of the equations in a way that magnetic charge can't? :wink:
     
  4. Apr 16, 2010 #3

    Cyosis

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    I believe you're missing a minus sign for the E-field. Grab your book and go to the page where the Maxwell equations are listed. Can you identify the equation that has electric charge as a source term?
     
  5. Apr 16, 2010 #4
    thanks, yes you are right the minus sign should be there.

    With regards to the second part, i think I have it thanks to your hints. Div B = 0 is the maxwell eqn that shows there are no magnetic monopoles (as there are no source terms - unlike for div E). The definition of the vector potential is consistent with this because the divergence of a curl is always zero.
     
  6. Apr 16, 2010 #5

    Cyosis

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    Yes that is correct.
     
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