Electrical Energy Electron Question

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SUMMARY

The discussion focuses on calculating the smallest possible distance between two electrons fired directly at each other at a speed of 3.5x10^6 m/s. The relevant parameters include the mass of an electron (me = 9.1x10^-31 kg) and the charge of an electron (qe = 1.6x10^-19 C). The conservation of energy principle is applied, where the initial kinetic energy (KE) of one electron is equated to the potential energy (PE) when they are at a distance x from the midpoint. The midpoint serves as a reference point for symmetry, allowing for a simplified calculation of the distance between the two electrons.

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Homework Statement


Two electrons are fired at 3.5x10^6 m/s directly at each other

a) calculate the smallest possible distance between the 2 electrons

me=9.1x10^-31 Ve1=3.5x10^6 m/s qe=1.6x10^-19 C

Homework Equations



Em1=Em2


The Attempt at a Solution



Tried using Em1=Em2 which 1/2meve1^2+kqeqe/r1=1/2meve2^2+kqeqe/r2

I can't seem to use that formula because both electrons are moving, instead of one being stationary.
 
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By symmetry, you only need to consider the energy for one electron. What is its initial KE, and what is its PE when a distance x from the midpoint between them?
 
So how would i calculate the distance between them if i could consider one electron?
 
As I said, work relative to the midpoint between them, which, by symmetry, is stationary.
 
that kind of confuses me, sorry but could you elaborate on the symmetry?
 
Let C be the midpoint. When one electron is distance x from it and moving towards it at speed v, the other will be distance x on the other side, also moving towards it at speed v. Each separately satisfies conservation of energy. The only thing to watch is that when you calculate the PE of one you measure distance from the other electron (2x), not from C.
 
Thanks sir! The help is much appreciated, with all the formulas in this unit, questions are quite confusing.
 

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