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?
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: [tex]F=k_e \frac{q_e q_e}{d^2} [/tex] So, in order for the additional electron to cross this point, it is required an infinite amount of work, which is impossible.
