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## Homework Statement

A very long, thin straight line of charge has a constant charge density of 2.0pC/cm. An electron is initially 1.0cm from the line and moving away with a speed of 1000km/s. How far does the electron go before it comes back?

## Homework Equations

ΔU = ΔV*q

ΔKE + ΔU = 0

ΔV = -2Kλln(rb/ra)

W = 2Kλqln(rb/ra)

W = -ΔU

## The Attempt at a Solution

first off:

2.0pC/cm = 200pC/m

1000km/s = 1x10^6m/s

KEa + Ua = KEb + Ub

1/2mv^2 + Ua = 0 + Ub

1/2mv^2 = Ub-Ua

1/2 * (9.1x10^-31)*(1x10^6)^2 = -ΔU

4.55x10^-19 = -ΔU

W = -ΔU

4.55x10^-19 = 2Kλqln(rb/ra)

4.55x10^-19 = 2K(200x10^-4)(1.6x10^-19)ln(rb/.01)

7.899x10^-9 = ln(rb) - ln.01

ln(rb) = 4.605

rb = 100m

Well, that is the process that I followed, and I feel like I did ok, except that the majority of the rest of my class got different answers. They all got .66m, which seems more realistic, 100m just seems too far. I have another question that again, I seem to get a different value than everyone else. I think I may be screwing up the conservation part in the beginning, but I have no idea where I'm going wrong. I asked my teacher, and he said to use ΔU = ΔV*q, but other than considering ΔV = -2Kλln(rb/ra) & W = 2Kλqln(rb/ra), I don't know where I would use it. Any help would be greatly appreciated.