Let V(x,y) be the electric potential associated to an electric field E. Suppose that V is harmonic everywhere on R^2. Let F(x,y) be some function such that V and F satisfy Cauchy-Riemann equations (so that F is the harmonic conjugate of V). Let f : C -> C such that f(x,y) = V(x,y) + iF(x,y) be a holomorphic (analytic) function in C. I'm aware that the level curves of V and F are orthogonal everywhere. What is the physical interpretation of F here? V is the potential, but would F be something like constant force curves? I mean, V is given and I understand its meaning, but F is "artificially" generated to satisfy Cauchy-Riemann equations. It does, however, smell strongly of the electric field force lines. Is my intuition right?