  We probe electric-field noise in a surface ion trap for ion-surface distances
$d$ between 50 and 300 $\mu\mathrm{m}$ in the normal and planar directions. We
find the noise distance dependence to scale as $d^{-2.6}$ in our trap and a
frequency dependence which is consistent with $1/f$ noise. Simulations of the
electric-field noise specific to our trap geometry provide evidence that we are
not limited by technical noise sources. Our distance scaling data is consistent
with a noise correlation length of about 100 $\mu\mathrm{m}$ at the trap
surface, and we discuss how patch potentials of this size would be modified by
the electrode geometry.
