How to Correctly Solve for the Minimum Distance Between Two Electrons?

[Jake357]

Homework Statement

An electron, having the initial velocity of 10^6 m/s, is approaching from a long distance another electron, which is free and at rest. Calculate the maximum force of interaction between the particles. The answer must be 2.26*10^-10 N

Relevant Equations

KE=mv^2/2
F=ke^2/d^2

I tried to make the kinetic energy of the first electron equal to the electric potential work.
mv^2/2=ke^2/d
We have to solve for the minimum distance between them: d=2ke^2/mv^2=5.05*10^-10 m
The force is: F=ke^2/d^2=9*10^-10 N, which is not correct.

 

[TSny]

The second electron is free to move. Will both electrons ever come to rest?

 

[Jake357]

The second electron is free to move. Will both electrons ever come to rest?

When the first electron has the known initial velocity the second electron is at rest (not moving) at a long unknown distance between them. And I think that when they will get the closest possible to each other they will still be moving, thus both having kinetic energy. So no, I don't think they will be at rest.

 

[TSny]

When the first electron has the known initial velocity the second electron is at rest (not moving) at a long unknown distance between them. And I think that when they will get the closest possible to each other they will still be moving, thus both having kinetic energy. So no, I don't think they will be at rest.

Yes. So, the initial KE is never completely converted into potential energy.

You might consider analyzing this problem form a different frame of reference that is moving relative to the original frame of reference.

If you want to keep the analysis in the original frame, then think about the relation between the velocities of the electrons when they are at minimum separation. Is there another conservation law besides energy conservation that could be helpful here?

 

[Jake357]

Yes. So, the initial KE is never completely converted into potential energy.

You might consider analyzing this problem form a different frame of reference that is moving relative to the original frame of reference.

If you want to keep the analysis in the original frame, then think about the relation between the velocities of the electrons when they are at minimum separation. Is there another conservation law besides energy conservation that could be helpful here?

I think the conservation of momentum also should be used.

 

[TSny]

I think the conservation of momentum also should be used.

Yes.