  In this article, we analyse an integral equation of the second kind that
represents the solution of $N$ interacting dielectric spherical particles
undergoing mutual polarisation. A traditional analysis can not quantify the
scaling of the stability constants -- and thus the approximation error -- with
respect to the number $N$ of involved dielectric spheres. We develop a new a
priori error analysis that demonstrates $N$-independent stability of the
continuous and discrete formulations of the integral equation. Consequently, we
obtain convergence rates that are independent of $N$.
