  Using an atomic force microscope as a local voltmeter, we measure the Hall
voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We
observe a linear profile in the bulk of the sample in the transition regions
between QH plateaus and a distinctly nonlinear profile on the plateaus. In
addition, localized voltage drops are observed at the sample edges in the
transition regions. We interpret these results in terms of theories of edge and
bulk currents in the QH regime.
