# Definition:Density (Physics)

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## Definition

**Density** is a physical quantity that is variously specified according to context.

Its general meaning is that of some physical quantity per unit volume, or area, or length.

### Mass Density

**Mass density** is a physical quantity.

The **mass density** of a body is its mass per unit volume.

### Area Mass Density

The **area mass density** of a two-dimensional body is its mass per unit area.

### Linear Mass Density

The **linear mass density** of a one-dimensional body is its mass per unit length.

### Electric Charge Density

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:

## Also see

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**density**:**2.** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**density**:**2.**