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The geometry of an atomically sharp or nearly atomically sharp tip in proximity to a planar anode may be closely approximated in the prolate‐spheroidal coordinate system. An exact three‐dimensional electrostatic‐potential solution for a free charge in such a tip/base junction is given in this letter, including calculations for both the symmetrical on‐axis case and the asymmetric off‐axis case. An exact solution for the potential‐energy barrier is also given; this solution has immediate applications in three‐dimensional tunneling studies and in calculations of electron trajectories in micron‐ and submicron‐sized field‐emitter arrays. © 1994 American Institute of Physics.