B Magnetic field at relativistic speed

Force: To get the force in the other frame, divide the center of mass force by gamma, force means here simply the force that effects the electrons. Force transforms in this simple way in this simple case.

Trajectory: The separation process is time dilated. To get the timetable of the separation process in the other frame, multiply the center of mass timetable by gamma.

 

1: I didn't check the link, until now. I am sure the total force changes by gamma, but the question wasn't about total force. But somehow I feel that the formula F=q*v*B should work even if v is relativistic.

2: A force on a projectile causes a bending of its trajectory. So trajectories are bent in this case.

 

Use the E and B transforms for SR

 

https://en.wikipedia.org/wiki/Class...rmation_of_the_fields_between_inertial_frames

 

You know what the Lorentz Force Law is? It is co-variant with SR, it applies in all cases. That is how we obtain the magnitude of the force.

In relativity Force = dp/dt where p is the relativistic momentum.

1) Yes, it cannot exceed 1.

2) It will deflect.

 

No, I'm just thinking about a wire loop, and the fact that the magnetic field of the loop is proportional to the current in the loop, and the current in the loop is proportional to the velocity of the moving charges in the loop, if the amount of moving charges is constant. So when we know the currents of two loops, we can calculate the magnetic force between the two loops very easily, without worrying about relativity

And we can also calculate very easily magnetic force between two straight wire segments, using Ampere's law, no relativistic corrections needed.

What happens after one second is the same what happens after 1/gamma seconds in the other frame. In other words: What happens in the non-rest frame is a slow-motion version of what happens in the rest-frame. In other words high speed motion causes time dilation.

 

Idk where you get those numbers from.

Both electric and magnetic forces are part of the Lorentz force.

The electric force will always exceed the magnetic force so they will always diverge.

 

You can always transform into the rest frame of the particles. In that frame they repel due to plain vanilla electrostatic repulsion. They must, therefore, repel in all frames, or else there is a contradiction. A frame is simply a point of view. You can't make things that are moving apart start moving together by changing point of view.

 

There is always a net repulsion. Your explanation for why this is so may vary. In one frame there is an electrostatic repulsion, while in another there is a stronger electrostatic repulsion and a weaker magnetic attraction.

Yes, you can figure out the rate of divergence in any frame. Probably the easiest way to do it is to work out the positions and/or velocities of the electrons as a function of time in their rest frame (more precisely the center of mass frame of the pair) and then transform those.

 

Not in my head. The forces in the diagram look plausible (there's a net repulsion) but I haven't checked them in detail.

Do you know how to calculate the electrostatic force between two charges? Coulomb's Law? If so, can you calculate the force on the two electrons if they are at rest (i.e. electrostatic repulsion only)?