Magnetic gradient drift (${\mathbf{v}}_{\nabla B}=\mu \mathbf{B}\times \nabla B/(q{B}^2)$)

A slowly varying field magnitude exerts the gyroaveraged force $-\mu \nabla B$ on a particle with magnetic moment $\mu =m{v}_{\perp }^2/(2B)$. Applying the perpendicular-force guiding-centre drift formula gives the displayed velocity. Its direction depends on the sign of the particle charge.