# Speed at which two charges collide

## Homework Statement

Point charge A of mass m for which q=-Q is held in place as point charge B of mass m for which q=+Q is released from rest at a distance x. What is the speed of charge B as it collides with charge a? (This isn't an actual problem we have, just something that I was wondering as we're starting E&M)

## Homework Equations

Fe=kqq/r^2

E=kqq/r

Potential energy = Kinetic energy

## The Attempt at a Solution

I started out with an a(x) equation but didn't get beyond that as I couldn't find how to work with functions of time instead of position. Can you do this by just converting the potential energy at rest to kinetic energy? I feel like there should be more to it because the acceleration goes to infinity as b gets closer and closer to a.

Just gave it some more thought and realized the U -> KE idea doesn't make sense (U increases as x decreases)... can anyone point me in the right direction?

Alright, new idea: would it be easier instead to find the time it takes for a positive charge to collide with a negative charge that is held in place a distance r away from where the positive charge starts?

It's probably easier to find the time it takes the moving charge to move from r to r-x away from the stationary charge, so to find it could we take the limit as x approaches r of some equation? I have no idea what that would be, though.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Point charge A of mass m for which q=-Q is held in place as point charge B of mass m for which q=+Q is released from rest at a distance x. What is the speed of charge B as it collides with charge a? (This isn't an actual problem we have, just something that I was wondering as we're starting E&M)

## Homework Equations

Fe=kqq/r^2

E=kqq/r

Potential energy = Kinetic energy

## The Attempt at a Solution

I started out with an a(x) equation but didn't get beyond that as I couldn't find how to work with functions of time instead of position. Can you do this by just converting the potential energy at rest to kinetic energy? I feel like there should be more to it because the acceleration goes to infinity as b gets closer and closer to a.
Hello djrkeys4. Welcome to PF !

I doubt that you will ever see this problem in a textbook. The potential energy → -∞ as x → 0 . Therefore, the kinetic energy → +∞ as x → 0 .
Alright, new idea: would it be easier instead to find the time it takes for a positive charge to collide with a negative charge that is held in place a distance r away from where the positive charge starts?

It's probably easier to find the time it takes the moving charge to move from r to r-x away from the stationary charge, so to find it could we take the limit as x approaches r of some equation? I have no idea what that would be, though.
I haven't worked it out, but I'm pretty sure that it is possible to find the time it takes for the particles to collide.