  We report spatially resolved measurements of static and fluctuating electric
fields over conductive (Au) and non-conductive (SiO2) surfaces. Using an
ultrasensitive `nanoladder' cantilever probe to scan over these surfaces at
distances of a few tens of nanometers, we record changes in the probe resonance
frequency and damping that we associate with static and fluctuating fields,
respectively. We find that the two quantities are spatially correlated and of
similar magnitude for the two materials. We quantitatively describe the
observed effects on the basis of trapped surface charges and dielectric
fluctuations in an adsorbate layer. Our results provide direct, spatial
evidence for surface dissipation in adsorbates that affects nanomechanical
sensors, trapped ions, superconducting resonators, and color centers in
diamond.
