Finding a scalar field given two gauge fields

[rwooduk]

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 into 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.

 

[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?

 

[rwooduk]

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?

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