The problem involves calculating the time it takes for an electron and a positron, initially at rest and separated by a distance R, to collide. The context is rooted in electrostatics and dynamics, particularly focusing on the forces acting between charged particles.
The discussion is ongoing, with participants exploring different interpretations of the problem and the implications of mass differences on the motion of the particles. Some guidance has been provided regarding the use of reduced mass and integration techniques, but no consensus has been reached on a definitive approach.
There is a noted confusion between the particles involved, initially referring to a proton instead of a positron, which has implications for the symmetry of the problem. Participants are also grappling with the effects of changing forces and acceleration on their calculations.
vela said:What do you get when you use F=ma?
The difference in masses breaks the symmetry. The proton won't move as far as the electron because it's so massive in comparison.gsingh2011 said:I don't know, acceleration is changing. Let say we have F=kq1q2/r2=ma. Since this problem is symmetrical, I was thinking the two particles would meet in the middle, so each would travel a distance of R/2.
The standard trick is to multiply by [itex]\dot{r}[/itex]. You'll find it makes both sides of the equation integrable, but first you need to find the correct equation.So I could divide by m and integrate twice to find the position function, and set that equal to R/2. The only problem with that idea is the force is changing with respect to r, so I can't integrate with respect to t. So I guess that method won't work.
It's a positron not a proton, so the mass is the same.The proton won't move as far as the electron because it's so massive in comparison.