The trajectories of charged particles, emitted from within or from the
close vicinity of pointed shaped surfaces, requires the knowledge of
the electric field resulting from the potential bias between surface a
nd detector, or screen. Frequently it is necessary the use of numerica
l methods for solving Laplace's equation as a result of difficulties i
n obtaining an analytical expression. Recently we have shown that, whe
n any two coordinate surfaces of an orthogonal system are kept at two
different but constant potentials, it is possible to obtain an analyti
cal solution for the potential in a relatively simple manner. Using th
is general property of orthogonal coordinate systems, we present the s
olution for the electric potential and field in the vicinity of pointe
d surfaces for several cases of practical interest in field emission,
field ionisation, atom-probe field ion spectroscopy and related phenom
ena.