Gauss’s Law

Gauss Law states that the total Electric Flux through a closed surface is equal to the total (net) electric charge inside the surface.

Why Gauss's Law?

We use it as an alternative to Coulomb’s Law.

• Provides us a different way to express the relationship between electric charge and electric field

$Q_{encl}={\oint }_{surface}\vec{D}\cdot d\vec{S}$ $\vec{D}$ is the Electric Flux Displacement Vector, $\vec{D}=ϵ\vec{E}$

Calculating Electric Field

We can use Gauss Law (sometimes) to calculate the electric field created. However, to do this, you must ensure that one really important property is met: it is a Gaussian Surface.

New Gauss Law Form

$\nabla \cdot \vec{D}={\rho }^{free}$ ${\varphi }_E=Q_{encl}^{free}={\oint }_{surface}\vec{D}\cdot d\vec{S}$