# Photoelectric effect and work function

In a photoelectric effect we remove electrons from a metal using high energy photons, the work function is the minimal energy required for this effect.

My question is why doesnt the work fucntion depended on time? The more electrons we take out from the metal, the more ionized it becomes (if we remove a lot of negative charge, it will turn positive), and as a result we would expect to need more energy for this effect (the possitive charge of the metal would make it harder to remove the remaining electrons). Why does the work function remains constant no matter how much electrons we take out?

The work function doesn't depend on time because we're assuming a $\textbf{steady state solution}$. This means the differential equations which describe the total charge on the surface of the metal are at an equilibrium, where all the time derivatives are $0$.