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.
Sources
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Introduction: Electromagnetic Theory
- 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.3$ Electric Fields in Matter: $1.3.1$ The atomic charge density