# Electric Charge Density

Yeldar
(src: Intro to Electrodynamics, Griffith, Problem 1.46a)
Q: Write an expression for the electric charge density $\rho (r)$ of a point charge $q$ at $r^'$. Make sure that the volume integral of $\rho$ equals $q$.

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

$$\rho(r)=\frac{q}{4*Pi*R^2}\delta(r-r^')$$

But, the problem I see with this, is that while yes, integrating this over any volume $V$ 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.

Staff Emeritus
Gold Member
I think that delta function should be 3D: $\delta^{(3)}(\vec{r}-\vec{r}')$. Note that the n-D delta function has dimensions of (length)-n.

Last edited:
Yeldar
Yeah, sorry missed that. Have the $\delta^3$ on my paper, just forgot to type it in.

I don't understand how n-D delta functions have a dimension of (length)-n, could you explain that perhaps?

Staff Emeritus
$$\int_{-\infty}^{\infty}\delta(x)dx=1$$