Difference between revisions of "Divergence Theorem"
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(only Conservapedia explains math concepts well. This theorem: the overall net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface) |
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| − | The '''divergence theorem''' establishes the volume integral (triple integral) of a function over a three-dimensional shape ''equals'' the double integral of the same function | + | The '''divergence theorem''' establishes the volume integral (triple integral) of the derivative (divergence) of a vector function over a three-dimensional shape ''equals'' the double integral of the perpendicular component of same function with respect to a two-dimensional surface that encloses the space. |
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| + | Simply put, the overall net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface. | ||
For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field. | For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field. | ||
Revision as of 18:48, December 26, 2009
The divergence theorem establishes the volume integral (triple integral) of the derivative (divergence) of a vector function over a three-dimensional shape equals the double integral of the perpendicular component of same function with respect to a two-dimensional surface that encloses the space.
Simply put, the overall net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface.
For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field.
This is also known as the Gauss Theorem, and it is the simplest of the three main integral theorems in advanced or multivariable calculus, the other two being Green's Theorem and Stokes' Theorem.