Helmholtz's Theorem
Any vector field 
satisfying
may be written as the sum of an irrotational part and a solenoidal part,
 |
(3) |
where
See also
Irrotational Field, Solenoidal Field, Vector Field
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References
Arfken, G. "Helmholtz's Theorem." §1.15 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 78-84, 1985.Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1084, 2000.
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Cite this as:
Weisstein, Eric W. "Helmholtz's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HelmholtzsTheorem.html