Why isn't electric potential infinite?

Question

In my textbook, I've read that electric potential is the work performed to carry one unit of positive charge to electric field from infinite distance.

We know that, W = Fs

So here the distance is infinity and W = F × infinity = infinity

But I have never seen potential's being infinity. So what is the problem here actually?

Answer 1

$W=Fs$ only when the force is constant. In general, $$ W=-\int_a^b \vec F\cdot d\vec r $$ for a path from $a$ to $b$. In the case of the electric potential, $$ W=-q \int_{\infty}^b \vec E\cdot d\vec r = -q\frac{Q}{4\pi\epsilon_0} \int_{\infty}^b \frac{1}{r^2}\cdot d\vec r=\frac{qQ}{4\pi\epsilon_0}\frac{1}{b} $$