A solution to the conduction equation has been developed for two equal
size, nonconducting spheres with the line between centers perpendicul
ar to the applied field. The solution, valid when the gap between the
spheres is small compared to their radius, is based on a matched asymp
totic expansion. For the case when the conductivity is uniform everywh
ere (i.e., Laplace's equation), the solution agrees well with numerica
l results obtained from an infinite series solution in bispherical coo
rdinates. An example with a nonuniform conductivity in the gap is pres
ented to demonstrate how the method can be extended to more general co
nduction problems. (C) 1997 American Institute of Physics.