An electron and a proton are held \(2 \mathrm{~m}\) apart. The midpoint between the electron and the proton sets the origin of a coordinate system, with the \(x\) axis pointing toward the proton.

(a) A second electron is moved to the origin from infinity. How much work does this take?

(b) Keeping the second electron fixed at the origin, a third electron is sent toward the origin with a velocity of \(400 \mathrm{~m} / \mathrm{s}\) from the location \((0 \mathrm{~m}, 10 \mathrm{~m})\). How close does this electron get to the origin?