# Density of an ionised gas

I have been wondering about this problem for quite some time now and any input is much appreciated. If a gas consisting of n atoms with individual mass m and charge q is put under an external pressure P what will the resulting density be? Assume spherical symmetry.

An illustration of the problem (The external pressure is supplied by an electrically charged sphere) The density of the gas must be
$$\rho = \frac{mn}{V_{gas}}$$

If there is an average space of a between the atoms (and lets assume that the atoms does not occupy any space) then the total space occupied by the gas is Vgas = $$n \cdot 4/3 \pi a^3$$.

The internal pressure of the gas must be equal to the external pressure.
Fext = Fint
PA = $$n \cdot \frac{1}{4 \pi \epsilon_0} \frac{q^2}{a^2}$$
From here its just substituting and expressing rho in terms of the stated variables.

Can someone please comment on my derivation, does it seem sound? I am most concerned with the application of Columbs law.

All the best
Mikkel