Electrical Energy Electron Question

[BlueCardBird]

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.

 

[haruspex]

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?

 

[BlueCardBird]

So how would i calculate the distance between them if i could consider one electron?

 

[haruspex]

As I said, work relative to the midpoint between them, which, by symmetry, is stationary.

 

[BlueCardBird]

that kind of confuses me, sorry but could you elaborate on the symmetry?

 

[haruspex]

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.

 

[BlueCardBird]

Thanks sir! The help is much appreciated, with all the formulas in this unit, questions are quite confusing.