# Finding a scalar field given two gauge fields

1. Dec 14, 2014

### rwooduk

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. Dec 14, 2014

### pasmith

You need to solve $$\frac{\partial \Phi}{\partial x} = \frac{By}{2}, \\ \frac{\partial \Phi}{\partial y} = \frac{Bx}{2}, \\ \frac{\partial \Phi}{\partial z} = 0.$$ Have you not had to solve such problems before?

3. Dec 14, 2014

### rwooduk

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