## Helmholtz's Theorem

Any Vector Field satisfying

 (1) (2)

may be written as the sum of an Irrotational part and a Solenoidal part,
 (3)

where for a Vector Field ,
 (4) (5)

Arfken, G. Helmholtz's Theorem.'' §1.15 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 78-84, 1985.