# How long after the decay do $e^{-}$ and $e^{+}$ Collide

1. Dec 9, 2015

### Potatochip911

1. The problem statement, all variables and given/known data
A particular type of fundamental particle decays by transforming into an electron $e^{-}$ and a positron $e^{+}$. Suppose the decaying particle is at rest in a uniform magnetic field of magnitude 3.53 mT and the $e^{-}$ and $e^{+}$ move away from the decay point in paths lying in a plane perpendicular to the magnetic field. How long after the decay do the $e^{-}$ and $e^{+}$ collide?

2. Relevant equations

3. The attempt at a solution

The period which is all we need to solve this problem can be found to be $T=\frac{2\pi m_{e}}{qB}$ for this problem. Personally I think these particles would collide at $t=T$ but in the solutions manual it says they collide at $t=T/2$. This doesn't entirely make sense to me since although both the particles are moving at a speed $v$ they won't have completed the entire rotation at $T/2$ although they will have travelled a total distance $2\pi r$

2. Dec 9, 2015

### haruspex

Maybe I'm missing something, but won't they collide after each has gone half way around the circle?

3. Dec 9, 2015

### Potatochip911

I understand the path they take now. I assumed that both electrons were traveling in the same direction at the start, in this case it will be T before they collide. But if the angle between the two speeds is 180 then it only takes T/2.