Helmholtz Decomposition
In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition. It is named after Hermann von Helmholtz.
This implies that any such vector field F can be considered to be generated by a pair of potentials: a scalar potential φ and a vector potential A.
Read more about Helmholtz Decomposition: Statement of The Theorem, Fields With Prescribed Divergence and Curl, Differential Forms, Weak Formulation, Longitudinal and Transverse Fields