Gauss's law
Also known as Gauss' law, Gauss law
foundational law of electromagnetism
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Gauss's law is a foundational rule of electromagnetism that relates electric charges to the electric fields they create around them. It matters because it provides a powerful mathematical way to calculate electric fields in situations with certain symmetries, and it's one of the core equations that describe how electricity and magnetism work.
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Gauss's law in its integral form is particularly useful when, by symmetry reasons, a closed surface (GS) can be found along which the electric field is uniform. The electric flux is then a simple product of the surface area and the strength of the electric field, and is proportional to the total charge enclosed by the surface. Here, the electric field outside (r > R) and inside (r < R) of a charged sphere is being calculated.
In electromagnetism, Gauss's law, also known as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the distribution of electric charge to the resulting electric field.