Category:Field Generated by Surface Charge Density

This category contains pages concerning Field Generated by Surface Charge Density:

Let $B$ be a body of matter.

Let $P$ be a point inside $B$ whose position vector is $\mathbf r$.

The electric field at $P$ generated by the surface charge density over $B$ is given by:

$\ds \map {\mathbf E} {\mathbf r} = \dfrac 1 {4 \pi \varepsilon_0} \int_{\text {all surfaces} } \dfrac {\paren {\mathbf r - \mathbf r'} \map \sigma {\mathbf r'} } {\size {\mathbf r - \mathbf r'}^3} \rd S'$

where:

$\d S'$ is an infinitesimal area element

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

$\map \sigma {\mathbf r'}$ is the surface charge density at $\mathbf r'$

$\varepsilon_0$ denotes the vacuum permittivity.