Harmonic conjugate of potential function

[Termotanque]

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?

 

[LightHero]

Yes, your intuition is correct. The function F is related to the electric field in that it serves as a measure of the strength of the electric field at each point. In other words, the higher the value of F at a given point, the stronger the electric field at that point. Thus, the level curves of F can be thought of as constant force curves.