Electrostatic Potential / Work Question?

[lightofthemoon]

Homework Statement

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. If a second electron is initially at 20 m on the x axis, and given an initial velocity of 350 m/s towards the origin, it does not reach it. How close to the origin does it come?

Homework Equations

U = k q1 q2 / r
W = q ∫ E dl
E = F / q
KE = .5mv^2

The Attempt at a Solution

[/B]
I'm not quite sure how to approach this problem...

Calculate potential energy of the second electron:
U = k q1 q2 / r
U = (k * (1.6 * 10^-19) ^2 / 19) - (k * (1.6 * 10^-19) ^2 / 21)
U = 1.16*10^-30

Calculate initial kinetic energy
KE = .5mv^2
KE = .5 * 9.11 * 10 ^-31 * 350^2
KE = 5.58 * 10^-26

Calculate work needed to be done to bring it to the origin
not very sure about this part
W = q ∫ E dl
since all of this is done on x-axis I think the equation will simplify to W = qEx ?
E = kq / r
E = (9 * 10^9 * 1.6 * 10^-19 / 21) - (9 * 10^9 * 1.6 * 10^-19 / 19)
E = -7.22 * 10 ^-12
W = 2.3* 10^-29

From here I'm not quite sure how to continue...

 

[lightofthemoon]

I got the right answer through U / qE = x
Answer was 1.004 m

But can someone explain why I didn't need to use the initial speed of the electron? (Or did I actually need it and just got the right answer by chance?) Thank you

 

[haruspex]

I got the right answer through U / qE = x
Answer was 1.004 m

But can someone explain why I didn't need to use the initial speed of the electron? (Or did I actually need it and just got the right answer by chance?) Thank you

It is not clear what you did to get the answer. In your original attempt you calculated the initial KE. Did you use that?
Please post all your working.

 

[lightofthemoon]

No, I didn't use the initial KE at all.

Work to bring the particle to the origin = qEx
So I set U=qEx and solved for x (how far it would get to the origin)
x = U / qE
E = kq / r E = (9 * 10^9 * 1.6 * 10^-19 / 21) - (9 * 10^9 * 1.6 * 10^-19 / 19)
E = -7.22 * 10 ^-12
U = k q1 q2 / r
U = (k * (1.6 * 10^-19) ^2 / 19) - (k * (1.6 * 10^-19) ^2 / 21)
U = 1.16*10^-30

1.16*10^-30 / (-1.6 * 10^-19 * -7.22 * 10 ^-12 ) = x
x = 1.004 m