Electric flux through closed surface via total charge

Known as Gauss’s law, it states that the electric flux through any closed surface \(S\) is equal to the total charge within volume \(V\) enclosed by that surface, and in the SI units, divided by the vacuum permittivity. The closed surface is also referred to as Gaussian surface.

Conditions:

1. \(S = \partial V\), i.e. surface \(S\) encloses volume \(V\). In other words, the surface must be closed.

Links:

1. Wikipedia.

total_electric_flux

electric_flux through surface \(S\).

Symbol:

Phi_E

Latex:

\(\Phi_\mathbf{E}\)

Dimension:

length*voltage

total_charge

Total charge inside volume \(V\).

Symbol:

q

Latex:

\(q\)

Dimension:

charge

law

Phi_E = q / epsilon_0

Latex:

\[\Phi_\mathbf{E} = \frac{q}{\varepsilon_0}\]