Equal and opposite electric fields?

[granpa]

electron one is moving directly toward stationary electron two. the field at electron one due to electron one is proportional to 1/d^2. but the field at electron two due to electron one is less because electron ones field is compressed. it would seem from this that the forces on the 2 particles arent equal and opposite.

now I can see that there will be some frame in which both particles are moving at the same speed and in which the forces will be equal and opposite but seems like it should hold for all frames. it probably does and I'm just overlooking something simple.

the magnetic field can't play a role since they are moving straight toward each other.

 

[Meir Achuz]

NIII does not always hold for EM interactions, because the EM field can have changing momentum. The magnetic field of electron one does enter, because the EM momentum depends on the integral of EXB,

 

[granpa]

thanks for the reply. I would never have figured that out myself. (not that I understand what it means but at least I know where to look now).

so the momentum of the field at any given point equals EXEXV?

this formula makes more sense since the particle might be moving through an external magnetic field in which case I assume EXB wouldn't hold.

 

[granpa]

speaking of moving fields, I've been thinking about what sort of equations to use to understand what a moving field would look like. it occurred to me that fluid dynamics might be useful. if a sphere appeared magically in a body of water the displaced water would move outward. the flow lines of this displaced water would look identical to electric field lines. one might be able to use this to figure out what the field would look like in the case where the sphere/charge is moving.

 

[granpa]

oh. now I am beginning to get it. its the same reason they give for charges producing light. an accelerating particles field takes time to adjust so in the meantime the forces arent balanced. momentum isn't conserved unless you assume that the field itself contains the missing momentum.

where did I just read that? it will come to me later.

 

[granpa]

here is where I read it:

http://en.wikipedia.org/wiki/Field_(physics )