Finding a scalar field given two gauge fields

  • Thread starter rwooduk
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  • #1
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Homework Statement


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


Homework Equations


B = ∇XA

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.
 

Answers and Replies

  • #2
pasmith
Homework Helper
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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?
 
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Likes rwooduk
  • #3
747
55
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?

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

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