The Helmholtz theorem states that any vector may be decomposed into an irrotational (curl-free) and a solenoidal (divergence-free) part under certain conditions (given below). More precisely, it may be written in the form:
where is a scalar potential and is a vector potential. By the definitions of scalar and vector potentials it follows that the first term on the right-hand side is irrotational and the second is solenoidal. The general conditions for this to be true are:
The curl of must also vanish at infinity.
|Date of creation||2013-03-22 17:59:40|
|Last modified on||2013-03-22 17:59:40|
|Last modified by||invisiblerhino (19637)|
|Synonym||fundamental theorem of vector calcululs|