Q: Write an expression for the electric charge density [itex] \rho (r)[/itex] of a point charge [itex]q[/itex] at [itex]r^'[/itex]. Make sure that the volume integral of [itex]\rho[/itex] equals [itex]q[/itex].

Now, Closest I can seem to come up with is:

[tex] \rho(r)=\frac{q}{4*Pi*R^2}\delta(r-r^')[/tex]

But, the problem I see with this, is that while yes, integrating this over any volume [itex]V[/itex] that enclosed the point charge will return q, but that q would have to have units of charge/unit_volume which just dosent make sense. Or am I missing something?

Any help would be appreciated.