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**1. Homework Statement**

Two electrons with 20eV are 20 nm a part are move horizontally. Ignore relativistic effects and assume no other external forces.

How far apart are they vertically after .00001 seconds?

**2. Homework Equations**

Coulombs Law (the force between the two electrons) F=Kq1q1/r^2

F=ma (to calculate the acceleration where m is the mass of the electron)

delta x = 1/2at^2 (no initial vertical velocity, can calculate the change in distance)

**3. The Attempt at a Solution**

So I can calculate the force between them using coulombs law, the acceleration by using F=ma, and then given a time, the change in x using the kinematic equation. I am pretending that one of the electrons is fixed so that I can just calculate how far one moves (which I am not sure if that is correct way to do it or not).

The problem is that as the electron moves away the force decreases (proportionally to r^2). So I can divide the time up into a bunch of time slices and recalculate the distance it moves with olddistance += 1/2 * kq1q2/(m*olddistance^2)*timestep^2, but this doesn't really get me a close form, and I am afraid that floating point precision is going to mess with my results.

Thus is there some way for me to integrate it and get a closed form. I think maybe I can setup the electric field and kind of do a line integral or something...

Thanks for any help!

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