  We consider the thermodynamic effects of an electrically charged impurity
immersed in a two-dimensional two-component plasma, composed by particles with
charges $\pm e$, at temperature $T$, at coupling $\Gamma=e^2/(k_B T)=2$,
confined in a large disk of radius $R$. Particularly, we focus on the analysis
of the charge density, the correlation functions, and the grand potential. Our
analytical results show how the charges are redistributed in the circular
geometry considered here. When we consider a positively charged impurity, the
negative ions accumulate close to the impurity leaving an excess of positive
charge that accumulates at the boundary of the disk. Due to the symmetry under
charge exchange, the opposite effect takes place when we place a negative
impurity. Both the cases in which the impurity charge is an integer multiple of
the particle charges in the plasma, $\pm e$, and a fraction of them are
considered; both situations require a slightly different mathematical
treatments, showing the effect of the quantization of plasma charges. The bulk
and tension effects in the plasma described by the grand potential are not
modified by the introduction of the charged particle. Besides the effects due
to the collapse coming from the attraction between oppositely charged ions, an
additional topological term appears in the grand potential, proportional to
$-n^2\ln(mR)$, with $n$ the dimensionless charge of the particle. This term
modifies the central charge of the system, from $c=1$ to $c=1-6n^2$, when
considered in the context of conformal field theories.
