  Cold ions trapped in the vicinity of conductive surfaces experience heating
of their oscillatory motion. Typically, the rate of this heating is orders of
magnitude larger than expected from electric field fluctuations due to thermal
motion of electrons in the conductors. This effect, known as anomalous heating,
is not fully understood. One of the open questions is the heating rate's
dependence on the ion-electrode separation. We present a direct measurement of
this dependence in an ion trap of simple planar geometry. The heating rates are
determined by taking images of a single $^{172}$Yb${^+}$ ion's resonance
fluorescence after a variable heating time and deducing the trapped ion's
temperature from measuring its average oscillation amplitude. Assuming a power
law for the heating rate vs. ion-surface separation dependence, an exponent of
-3.79 $\pm$ 0.12 is measured.
