Three electrons and one proton are at rest, all at an approximate infiitne distance away from each
other. This original arrangment of the four particles is defined as having zero electrical potential
energy.
(a) How much work is required to bring one electron from infitinty to a location defined as the
origin, while the other three particles remain at infiniuty?
(b) Now, with the electron remaining fixed at the origin, how much work is required to bring one of
the remaining electrons from infinity to within a distance of 1.00 m from the first electron? The
other two particles remain at infinity. If this second electron was subsequently released, how fast
would it be traveling once it returned to infinity?
(c) Now, considering the two electrons fixed 1.00 m apart, how much work is required to bring the
third electron from infinity to within a distance of 1.00 m from both fixed electrons? This would
form an equilateral triangle of electrons. The proton remains at infinity. If this third electron was
subsequently released, how fast would it be traveling once it returned to infinity?
(d) Now considering the three fixed electrons forming an equilateral triangle 1.00 m to a side, how
much work is required to bring the leftover proton from infinity to a location exactly in the center
of the triangle? If this proton was subsequently released what would its motion look like?
(e) Now, if one electron is released from the triangle, where will it arrive after it returns to zero
potential energy, and what will be its final velocity?
(f) In this final arrangement of two fixed electrons and one fixed proton, with the third electron
gone, what is the potential energy of the proton?