  There are many interesting problems about the electrostatic potential of
finitely many charges. We consider one of them concerning the intensity of the
field, in other words, about the magnitude of the gradient of this potential.
We want to give a sharp estimate of the size of the set of points where this
gradient is large. Of course we want the estimate to be sharp in number $N$ of
charges. The size will be measured by the Hausdorff content with various gauge
functions. Such a setting allows us to consider a wide class of measures (not
necessarily with finitely many charges). The main technique will be
Calder\'on-Zygmund capacities and nonhomogeneous Calder\'on-Zygmund operators.
Here we establish a relationship between various types of capacities with
singular kernels (e. g. analytic capacity, lipschitz harmonic capacity, etc)
and non-linear capacity from the theory of potential \'a la Adams, Hedberg,
Havin, Maz'ya, Wolff. "Capacitary" part of the paper extends the theorem of
Mateu, Prat and Verdera [J. reine und angew. Math., 578 (2005), 201--223].
"Size estimates" part of the paper extends the theorem of M. Anderson and V.
Eiderman [Annals of Math., 163 (2005), 1057--1076]. The difficulty lies in the
fact that we cannot use Menger's curvature anymore because we are working in
spaces of dimension bigger than two.
