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
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.