A conservative vector field (for which the curl del xF = 0) may be assigned a scalar potential ϕ(x, y, z) - ϕ(0, 0, 0) congruent - integral_C F·d s = - integral_(0, 0, 0)^(x, 0, 0) F_1(t, 0, 0) d t + integral_(x, 0, 0)^(x, y, 0) F_2(x, t, 0) d t + integral_(x, y, 0)^(x, y, z) F_3(x, y, t) d t, where integral_C F·d s is a line integral.

line integral | potential function | vector potential