The velocity distribution and the density near a particle of an equilibrium one component plasma

The equation governing the conditional relative velocity distribution of an equilibrium one component plasma at distances smaller than the interparticle distance is derived from elementary principles of classical dynamics and probability, the latter defined from the temporal point of view. It becomes obvious that in accordance with todays accepted views the maxwellian velocity distribution satisfies the above equation. Using this result it is also shown that the conditional number density has the form n(r) = n₀exp(-e²/rk_BT).