In the wikipedia page for guiding center,the following lines are written about curvature drift of charged particles.

My problem is the part that tells curl of B is zero in a vacuum.
Although I know Maxwell equations permit such a situation(with [itex]\vec{B}=\vec{B}(\mbox{only space variables}) \ and \ \vec{E}=0 [/itex]),I don't understand how that can happen.
Obviously a current has caused the existence of the magnetic field and so there should be a changing electric field.But there is no electric field and that seems strange to me.
I'll appreciate any ideas.
Thanks

Maxwell's equation relates curl of B to density and to the time derivative of E. If you are in a region that as no currents (i.e., away from wires) and the fields are static (no time variation), then curl B = 0.

Well,I know that.
The problem is, how can the electric field be static when there is a current?(I know that we're assuming no current at the point we're calculating the curl of B at.But a current elsewhere produces a changing electric field everywhere.)

The current can be static--a DC current from a battery, for instance. Or there may be no current at all, as when the magnetic field in your source-free region arises from a permanent magnet. Either way, J=0 in the vacuum and [itex]\frac{\partial \mathbf E}{\partial t}=0[/itex].

Somewhere should be sources of the magnetic field. In the static case you have
[tex]\vec{\nabla} \times \vec{H}=\vec{j}+\frac{1}{c} \vec{\nabla} \times \vec{M},[/tex]
where [itex]\vec{M}[/itex] is the magnetization of your permanent magnet. Of course, everywhere else, the curl vanishes, and there you can have locally a potential. Other than the elecric field a magnetic field can never be globally a gradient field!