  The electric double layer structure in an electrolyte close to a solid
substrate near the three-phase contact line is approximated by considering the
linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical
approach complements the semi-analytical solutions reported in the literature
by providing easily available characteristic information on the double layer
structure. In particular, the model contains a length scale that quantifies the
distance from the fluid-fluid interface over which this boundary influences the
electric double layer. The analysis is based on an approximation for the
equipotential lines. Excellent agreement between the model predictions and
numerical results is achieved for a significant range of contact angles. The
length scale quantifying the influence of the fluid-fluid interface is
proportional to the Debye length and depends on the wall contact angle. It is
shown that for contact angles approaching 90{\deg} there is a finite range of
boundary influence.
