An electron and proton are attached to an x axis, with the electron at x = +1.00

Question

An electron and proton are attached to an x axis, with the electron at x = +1.00m and the proton at -1.00m.

(a) How much work is required to bring an additional electron from infinity to the origin of the axis.

(b) if, instead of the second electron coming in from infinity, its initially at x = +20.00m on the x axis and is given an initial velocity of 500.0m/s toward the origin, does it reach the origin? If so, what is its speed the instant it reaches the origin? If not, how close to the origin does it come.

Explanation / Answer

as origin is equally distant from proton and electron so potential at origin = 0

a) work = 0

b) initial energy = 0.5 x 9.1 x 10-31 x 5002 + 9 x 109 x (1.6 x 10-19)2/19 - 9 x 109 x (1.6 x 10-19)2/21

= 1.137512 x 10-25 J

let closest approch is y m from electron

then energy , 1.137512 x 10-25 = 9 x 109 x (1.6 x 10-19)2/y - 9 x 109 x (1.6 x 10-19)2/(y+2)

493.71 = 1/y - 1/(y+2)

493.71(y2 +2y) = 2 => y = 0.002023427 m

so distance from origin = 1+ 0.002023427 = 1.002023427 m

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