Potential energy of a charge in a magnetic quadrupole field

I have a charged particle of charge $q$ that moves with velocity $vec{V}$ from a position $vec{r}$, inside a magnetic quadrupole field of the form: $$vec{B}=B_{0}(x,y, -2z)$$
The Lorentz force acts upon this particle: $$vec{f}_{Lorentz}=qvec{V}timesvec{B}=qB_0[(-2V_{y}z-V_zy)hat{x}+(V_zx+2V_xz)hat{y}+(V_xy-V_yx)hat{z}]$$
I know the trajectory and velocity of the particle as a function of time $(hat{r}(t)$, $hat{V}(t))$, but I can’t manage to find the potential of this force. I suppose that I should use the integral $V_{Lorentz}=-int{vec{F}_{Lorentz}dot{}dvec{r}}$, But i’m not sure how or if maybe I could get a closed expression for this potential.

Thanks!