Symbols:Greek/Rho/Electric Charge Density

Electric Charge Density

$\map \rho {\mathbf r}$

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:

The $\LaTeX$ code for \(\map \rho {\mathbf r}\) is \map \rho {\mathbf r} .