Category:Electric Flux out of Closed Surface

This category contains pages concerning Electric Flux out of Closed Surface:

Electric Flux out of Closed Surface surrounding Point Charge

Let $q$ be a point charge.

Let $S$ be a closed surface surrounding $q$.

The total electric flux through $S$ is given by:

$F = \dfrac q {\varepsilon_0}$

Electric Flux out of Closed Surface surrounding Assemblage of Point Charges

Let $Q = \set {q_1, q_2, \ldots}$ be a set of point charges.

Let $S$ be a closed surface surrounding $Q$.

The total electric flux through $S$ is given by:

$\ds F = \dfrac 1 {\varepsilon_0} \sum_Q q_i$

Electric Flux out of Closed Surface surrounding Body with Continuous Charge Distribution

Let $B$ be a body of matter which has a continuous macroscopic charge density $\map \rho {\mathbf r}$.

Let $S$ be a closed surface surrounding $Q$.

The total electric flux through $S$ generated by the electric charge on $B$ is given by:

$\ds F = \dfrac 1 {\varepsilon_0} \int_V \map \rho {\mathbf r} \rd \tau$

where:

$V$ is the total volume enclosed by $S$

$\d \tau$ is an infinitesimal volume element

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

$\map \rho {\mathbf r}$ is the macroscopic charge density of the macroscopic electric field at $\mathbf r$

$\varepsilon_0$ denotes the vacuum permittivity.