Lorentz force between two moving charges

[Universeer]

Two charges are moving mutually perpendicular to each other in space with constant velocities.

The moment one charge crosses over the line of path of second charge the force on 1st charge (located just behind the 2nd charge moving away from it) appear to be zero (Magnetic field due to 2nd charge along its line of path is zero) while force on second charge due to 1st is non zero!
That violates Newton's 3rd law.

What am i missing here?

 

[Nugatory]

It might be easier to see what is going on if you work in a frame in which one of the particles is at rest. Compare with the frame in which the other is at rest.

 

[A.T.]

Summary: Lorentz force between moving Charges, violates Newton's 3rd law.

Two charges are moving mutually perpendicular to each other in space with constant velocities.

The moment one charge crosses over the line of path of second charge the force on 1st charge (located just behind the 2nd charge moving away from it) appear to be zero (Magnetic field due to 2nd charge along its line of path is zero) while force on second charge due to 1st is non zero!
That violates Newton's 3rd law.

What am i missing here?

1) You have to look at the total EM-force, not just the magnetic component.

2) Newton's 3rd law in the sense of instantaneous forces in fact doesn't always apply for EM-interactions. But it does apply in the more general sense of momentum conservation, if you account for the momentum in the EM-field.

 

[Universeer]

2) Newton's 3rd law in the sense of instantaneous forces in fact doesn't always apply for EM-interactions. But it does apply in the more general sense of momentum conservation, if you account for the momentum in the EM-field.

Can you Give an example?
I'll look for total EM force part

Thanks.

 

[Ibix]

Can you Give an example?

Two wires, one carrying a current and one not. Turn on the current in the "off" wire. It immediately feels a force from the magnetic field of the other wire, but it takes finite time for the magnetic field from the new current to reach the other wire. If you don't account for the momentum carried by the field you get a short period where one wire is accelerating and the other isn't.

It's analogous to me throwing a ball to you. If you forget about the momentum of the ball then my reaction to throwing the ball and your reaction to catching it both apparently violate momentum conservation. But that's because you forgot about the momentum of the "force carrier".