(c) Volume Charge Density

When a total charge q is distributed UNIFORMLY throughout the entire volume V of a body (Fig. 10.24), the VOLUME CHARGE DENSITY $\rho$ is defined as the charge per unit volume: $\rho=\frac{q}{V}.$ Its SI unit is coulomb per cubic metre ($\text{C/m}^3$). Typical physical examples of a volume charge distribution include charge spread uniformly throughout the entire body of a solid charged plastic sphere, or a solid charged plastic cube -- as opposed to a surface distribution, where the charge sits only on the OUTER skin of the object.

If the charge is instead distributed NON-uniformly throughout the volume of the material (so $\rho$ itself varies from point to point inside the body), the small element of charge dq contained within a small element of volume dV at any particular interior point is written as $dq=\rho\,dV,$ where $\rho$ is now understood as the LOCAL volume charge density at that specific point inside the body. …