  Starting with general semiclassical equations of motion for electrons in the
presence of electric and magnetic fields, we extend the Chambers formula to
include in addition to a magnetic field, time-dependent electric fields and
bands with Berry curvature. We thereby compute the conductivity tensor
${\sigma}_{{\alpha}{\beta}}(B,{\omega})$ in the presence of magnetic field for
bands in two (2D) and three (3D) dimensions with Berry curvature. We focus then
on several applications to magnetotransport for metals with Fermi surface
topological transitions in 2D. In particular, we consider a rectangular lattice
and a model related to overdoped graphene, to investigate the signatures of
different types of Fermi surface topological transitions in metals in the Hall
coefficient, Hall conductivity ${\sigma}_{xy}$ and longitudinal conductivity
${\sigma}_{xx}$. The behavior of those quantities as a function of frequency,
when the electric field is time dependent, is also investigated. As an example
of non-zero Berry curvature, we study the magnetotransport of the Haldane model
within this context. In addition, we provide the linear and nonlinear electric
current formula to order $E^2$.
