# Definition:Electric Charge Density

## Definition

Let $A$ be a point in space in which an electric field acts.

Let $\delta V$ be a volume element containing $A$.

The (electric) charge density $\map \rho {\mathbf r}$ at $A$ is defined as:

 $\ds \map \rho {\mathbf r}$ $=$ $\ds \lim_{\delta V \mathop \to 0} \dfrac Q {\delta V}$ $\ds$ $=$ $\ds \dfrac {\d Q} {\d V}$

where:

$Q$ denotes the electric charge within $\delta V$
$\mathbf r$ denotes the position vector of $A$.

Thus the electric charge density is the quantity of electric charge per unit volume, at any given point in that volume:

### Symbol

The usual symbol used to denote electric charge density is $\rho$ (Greek letter rho).

### Dimension

The dimension of electric charge density is $\mathsf {I T L}^{-3}$: electric charge per unit volume.

### Units

The SI units of electric charge density are $\mathrm C \, \mathrm m^{-3}$ (coulombs per cubic metre).

## Also known as

Electric charge density can also be referred to as charge density if it is understood that electric charge is the quantity under discussion.

## Also see

• Results about electric charge density can be found here.