Gauss's Law
Electricity & Magnetism > Electric field
Gauss's law Electric field is zero inside a conducting shell is derived from Gauss's law

"The net flux of an electric field through a Gaussian surface is equal to the net charge enclosed within the surface divided by the permittivity of free space".

In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law in simple terms states that : electric flux through any closed surface is proportional to the enclosed electric charge.

To apply Gauss' law one has to obtain the flux through a closed surface. The convention used to define the flux as positive or negative is that the angle must be measured with respect to the perpendicular erected on the outside of the closed surface: field lines leaving the volume make a positive contribution, and field lines entering the volume make a negative contribution.

Any "inverse–square law" can be formulated in a way similar to Gauss's law. For example, Gauss's law itself is essentially equivalent to the inverse–square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse–square Newton's law of gravity.

Gauss's law can be used to demonstrate that there is no electric field inside a Faraday cage with no electric charges. Gauss's law is something of an electrical analogue of Ampère's law, which deals with magnetism. Both equations were later incorporated into Maxwell's equations.