  We study a two-dimensional system of dipolar hard disks in the presence of a
uniform external electric field $\boldsymbol{\mathcal{E}} $ by Monte Carlo
simulations in a square with periodic boundary conditions. The study is
performed in both the fluid at high temperature and the phase of living
polymers at low temperature. In the considered geometry the macroscopic Maxwell
field $ \mathbf{E}$ is computed and found to be equal to the external field
$\boldsymbol{\mathcal{E}} $ in both phases. The dielectric properties of the
system in the liquid phase as well as in the polymeric phase are investigated.
