  The expression for the Debye shielding in plasma physics is usually derived
under the assumptions that the plasma particles are weakly coupled, so their
kinetic energy is much larger than the potential energy between them, and that
the velocity distributions of the plasma species are Maxwellian. The first
assumption also establishes that the plasma parameter ND, the number of
particles within a sphere with a Debye radius should be greater than 1, and
determines the difference between weakly and strongly coupled plasmas. Under
such assumptions, Poisson's equation can be linearised, and a simple analytic
expression obtained for the electrostatic potential. However, textbooks rarely
discuss the accuracy of this approximation. In this work we compare the
linearised solution with the exact one, obtained numerically, and show that the
linearisation, which underestimates the exact solution, is reasonably good even
for ND ~ 40. We give quantitative criteria to set the limit of the
approximation when the number of particles is very small, or the distance to
the test charge too short.
