Category:Macroscopic Charge Density

This category contains results about Macroscopic Charge Density.

Let $B$ be a body made out of an electrically conducting substance.

Let $\delta V$ be a volume element which is smaller than the scale used for a macroscopic electric field, but still large enough to contain many atoms.

Let $P$ be a point in the vicinity of $\delta V$ whose position vector is $\mathbf r$.

The macroscopic charge density is the charge density of the macroscopic electric field at $P$, defined as:

$\ds \map \rho {\mathbf r} = \dfrac 1 {\delta V} \int_{\delta V} \map {\rho_{\text {atomic} } } {\mathbf r'} \rd \tau'$

where:

$\d \tau'$ is an infinitesimal volume element

$\mathbf r'$ is the position vector of $\d \tau'$

$\map {\rho_{\mathrm {atomic} } } {\mathbf r'}$ is the atomic charge density caused by the electric charges within the atoms that make up $B$.