A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F congruent 0. Therefore, there exists a G such that F = del xG. Furthermore, F can be written as F | = | del x(T r) + del ^2(S r) | congruent | T + S, where T | congruent | del x(T r) | = | -rx( del T) S | congruent | del ^2(S r) | = | del [d/(dr)(r S)] - r del ^2 S.

Beltrami field | divergence | irrotational field | solenoidal field | toroidal field | vector field