The Koch curve is used in the problem of evaluating and characterizing the
electric equipotential lines in the infinite semi-space limited by a rough
conducting one-dimensional surface. The solution of Laplace's equation subj
ect to a constant potential difference between the curve and a straight lin
e placed at infinity is performed with the help of Liebmann's method, The f
ractal dimension, D-f, of the equipotentials is numerically evaluated with
a box-counting method. It is found that D-f decays exponentially with dista
nce, from the value D-f = 1.273 at the Koch curve to the D-f = 1.0 when the
equipotentials become flat smooth lines. The method does not depend on the
specific choice of the Koch curve to model the rough substrate.