What is the Stokes Theorem
The Gaussian and Stokes law for vector fields are indispensable in electrodynamics. They provide a tool that makes working with Maxwell's equations much easier. The Gaussian theorem represents a relation between a vector field and its divergence, the Stokesian theorem does this for the rotation.
First, let us define the divergence of a vector field as a scalar field as follows:
The rotation of a vector field is again a vector field. The component of the vector field is in the direction of any unit vector defined by:
The Gaussian theorem
The Gaussian theorem says the following:
Now the proposition still has to be proven: Let it be the volume in small partial volumes divided up. The following applies:
Stokes' theorem is similar to Gaussian:
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