Calculate Min Distance of 2 Electrons Fired at Speed v

[shawshank]

electron together

2 electrons are fired at speed v towards one another. Knowing that each electron has a charge of e an mass m, what is the minimum distance that the two electrons will reach after fired at one another?

My book has a different answer than me so I have to check with you guys.

I wrote, -dE = dEk

-(E2 - E1) = (Ek2 - Ek1) - Ek2 is zero to for minimizing radius, and we assume E1 to be zero.

E2 = Ek1

2ke^2/r =mv^2

2ke^2 / mv^2 = r

Now in our book, they had this question with numbers, i derived this formula and plugged in my values and it didn't match the answer in the book.

 

[shawshank]

i never get any answers here man :(

 

[shawshank]

no luck?

 

[Astronuc]

It seems that the electric potential energy is correct, but using conservation of energy, that would have to equal the combined initial kinetic energies of the two electrons, which would be 2 * 1/2 mv² = mv².