Definition:Density (Physics)

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.

Mass density is a scalar quantity.

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

• Results about density in the context of physics can be found here.

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.