Suppose we have
$$V_1 = 0, \ A_1 = \frac{B}{2}(-y,x,0)$$
and
$$V_2 = 0,\ A_2=B(0,x,0)$$
I need to show that the potentials are equivalent and they represent the same magnetic and electric fields and find the gauge transformation that relates them.
So from what i know if we want to use gauge transformation:
$$v_2=v_1+\beta$$ $$A_2=A_1+\alpha$$
obviously then $\alpha = \nabla \lambda=\frac{B}{2}(y,0,0)$
But this whole thing just seems to easy. I also tried to compute the curl of the B field and integrate to get individual components but got something that didn't make any sense to. me. What am i doing wrong?