Is the Magnetic Vector Potential Dependent on a Constant Vector?

[Poop-Loops]

Homework Statement

It's problem 2.b) on this page:

http://www.phys.washington.edu/users/schick/322A/322-08ps3.pdf

The Attempt at a Solution

So, what it looks like to me, since the only terms in the actual vector potential are all multiplied, Lambda would have to be a constant, so that when you take the gradient of it, it becomes 0 and doesn't change A'. So basically A=A' and Lambda = some constant vector.

If Lambda wasn't constant, then taking the gradient would give some additional terms added to A, whereas no addition takes place.

 

[pam]

Write A' in Cartesian coords.
Take the difference D=A-A'.
It should be easy to show that D is a gradient.