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Cairrd
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Can anyone help me with how to derive Gauss's law (differential form) from the Divergance theorem?
Starting from where? Can you use the integral form of Gauss's law to begin?Cairrd said:Can anyone help me with how to derive Gauss's law (differential form) from the Divergance theorem?
Gauss' derived through Divergence is a mathematical theorem that relates surface integrals of a vector field to volume integrals of the divergence of the same field. It is also known as Gauss' theorem or the divergence theorem.
The theorem was discovered by German mathematician and physicist Carl Friedrich Gauss in the early 19th century. However, it was also independently discovered by French mathematician Siméon Denis Poisson around the same time.
Gauss' derived through Divergence is an important tool in vector calculus and mathematical physics. It allows for the simplification of surface and volume integrals and is used in the study of various physical phenomena, such as fluid dynamics and electromagnetism.
The theorem has many applications in fields such as engineering, physics, and mathematics. For example, it can be used to calculate the flux of a fluid through a surface or to find the electric charge enclosed within a given volume. It is also used in the study of fluid flow, heat transfer, and electromagnetism.
While Gauss' derived through Divergence is a powerful tool, it does have some limitations. It can only be applied to vector fields that are continuously differentiable and do not contain singularities. Additionally, it is only valid in three-dimensional space and cannot be extended to higher dimensions.