# Charge density

1. Feb 9, 2013

### Nikitin

Let's say you have a sphere which has a charge distribution where the charge behind a radius r can be expressed as Q(r). You also have the volume formula for a sphere, V(r).

Why is ρ, the charge density, defined as: ρ=dQ(r)/dV(r) instead of simply ρ=Q(r)/V(r)?

2. Feb 9, 2013

### voko

By integrating the density over some volume, you should get the total charge in that volume. Which of the two expressions satisfies that?

3. Feb 9, 2013

### Nikitin

Why can't you just integrate ρ(r) over a volume, with ρ(r) = Q(r)/V(r)?

4. Feb 9, 2013

### voko

Is $\int \rho(r) dV = \int \frac {Q(r)} {V(r) } dV$ equal to Q? What about $\int \rho(r) dV = \int \frac {dQ(r)} {dV(r) } dV$?

5. Feb 10, 2013

### Nikitin

I see it now. In the future, am i always supposed to use infinetesimal amounts for stuff like this?

6. Feb 10, 2013

### voko

It is hard to tell what you mean by "stuff like this", buy generally densities and concentrations are derivatives of some quantity with regard to volume (or mass), so that their integrals over some volume (or mass) restore the original quantity. If in doubt, just use this check.