# I Force less when charge particles move inline w/ each other?

1. Aug 14, 2016

### Chris Frisella

You have two electrons held at a fixed distance X from each other. You measure the opposing force is Y. Now you bring the electrons closer to each other, and then let them go so they can fly apart. As the electrons move apart and reach distance X, will the opposing force still be Y, or will it be less/more than that? Similarly, if you reserves it so you had the particles approaching each other (let's say electron & positron pair), what would happen with the force between them at distance X?

Put simply, does the speed towards or away from each other effect force?

2. Aug 14, 2016

### Staff: Mentor

Yes, the speed does affect the force. If you want to calculate this the Lienard Wiechert potentials will let you calculate the fields, and then the Lorentz force will give you the force.

So, in units where c=1 and q=1, if you have a charge A at x=-1 and a charge O at the origin then the force on O is f=(1,0,0). Now, if charge A is moving uniformly towards the origin at v=0.6 then f=(0.64,0,0). In that moving case, because you specified motion exactly towards the other charge there is no magnetic field at O, so the force on O does not depend on the speed of O, only the speed of A. (That is not a general result, but a very specific result only for the geometry specified)

3. Aug 14, 2016

### Chris Frisella

Thanks! I think I get the math, but I'm a little unfamiliar, so if the particles were moving apart at the same rate in your example, the reduction in force would be the same as well?

Last edited: Aug 14, 2016
4. Aug 14, 2016

### Staff: Mentor

Yes, it works out the same, but again that is dependent on the geometry specified. If they are not moving on a direct line then towards or away can make a difference.

5. Aug 14, 2016

### Chris Frisella

Ok, cool! Now comparing them moving apart vs moving towards each other, but in both cases not on a perfectly direct line (just slightly off). If my understanding of the fields is correct, the moving apart scenario wouldn't experience as much a decrease in force as the moving towards, yes?

Last edited: Aug 14, 2016
6. Aug 14, 2016

### Staff: Mentor

At this point you may want to try working this out for yourself. Do you have any math software? If so, then you can write a little routine to calculate the Lienard Wiechert potentials. If not, then use pencil and paper but look for very simple scenarios.

7. Aug 14, 2016

### Chris Frisella

Was just doing that :) SO actually it looks like I had that backwards, yea?

8. Aug 14, 2016

### Staff: Mentor

That is good! I will have to check later, I don't know that result off the top of my head so I will have to run it through my own routine.

9. Aug 14, 2016

### Chris Frisella

Cool, thanks! I'm interested to see what you get!

10. Aug 14, 2016

### Staff: Mentor

OK, so for O at the origin A at (-1,0,0) and for velocity of O = v and velocity of A = -v with v = (.6,.1,0) I get f=(0.633174, 0.0383742, 0.) and with v=(-.6,.1,0) I get f=(0.633174, -0.0383742, 0.)

11. Aug 14, 2016

### Chris Frisella

So, no difference. Do you know if that aligns with empirical data?