Found my problem; the issue at hand was I was being too mathematician-y :P
The problem is that this particular choice of function, f(x,y,z) (above), is not a valid gauge transform for this system. Gauge transforms (as it clearly says in merzbacher) must PRESERVE the resulting magnetic field...
Homework Statement
So I was doing a problem out of Merzbacher 3rd edition (end of chapter 4 problem 3); the homework set has already been turned in but I wanted to run this by you all and see what you thought.
I am essentially working with a particle in a 1-d ring constrained to the x-y plane...