Qualitative Description of The Law
In words, Gauss's law states that:
- The electric flux through any closed surface is proportional to the enclosed electric charge.
Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity. In fact, 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 all electric fields inside a Faraday cage have an electric charge. Gauss's law is something of an electrical analogue of Ampère's law, which deals with magnetism.
The law can be expressed mathematically using vector calculus in integral form and differential form, both are equivalent since they are related by the divergence theorem, also called Gauss's theorem. Each of these forms in turn can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge, or in terms of the electric displacement field D and the free electric charge.
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