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Finding a scalar field given two gauge fields

  1. Dec 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Demonstrate the equivalence between the gauge fields A1=(0,bx,0) and A2=)-yB/2,xB/2,0) and find the scalar field Φ for which A1= A2 + ∇Φ


    2. Relevant equations
    B = ∇XA

    3. The attempt at a solution
    The first part is fine, you just plug it in to the above relevant equation and you get Bk for each. But I am unsure of the second part. I tried

    A1 = A2 + ∇Φ ->>>

    ∇Φ = A1 - A2

    Φ = (∫ yB/2 dx , ∫ (Bx - xB/2) dy, ∫ 0 dz)

    but it was marked wrong with a "Φ is scalar!" comment.

    it's probably really simple but just stuck on it.

    as always thanks for any suggestions.
     
  2. jcsd
  3. Dec 14, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    You need to solve [tex]
    \frac{\partial \Phi}{\partial x} = \frac{By}{2}, \\
    \frac{\partial \Phi}{\partial y} = \frac{Bx}{2}, \\
    \frac{\partial \Phi}{\partial z} = 0.
    [/tex] Have you not had to solve such problems before?
     
  4. Dec 14, 2014 #3

    ahh i remember now, it was covered in last years math, will dig out my notes. Thank you!
     
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