# Finding a scalar field given two gauge fields

## 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

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.

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?
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?