Question

An electron and a proton are held on an x axis, with the electron at x = + 1.000 m and the proton at x = - 1.000 m. How much work is required to bring an additional electron from infinity to the origin?

Answer 1

It is required an infinite work. The additional electron will never reach the origin.

In fact, assuming the additional electron is coming from the positive direction, as it approaches x=+1.00 m it will become closer and closer to the electron located at x=+1.00 m. However, the electrostatic force between the two electrons (which is repulsive) will become infinite when the second electron reaches x=+1.00 m, because the distance d between the two electrons is zero:

`F=k_e (e q)/(r^2)`

So, in order for the additional electron to cross this point, it is required an infinite amount of work, which is impossible.