Solving Magnetic Field Force: Observer I vs Observer II

[physicsManiac]

i have 2 questions regarding magnetic field...
1)if 2 identical charges move parallel to each other(along y axis) with relative velocity zero the the observer I moving along with the charges will observe force along one direction only(along x-axis electrostatic) whereas an observer II(standing at origin) watching the charges move away will observe a force on charges along both x and y direction(x and y-axis both i.e magnetic and electrostatic).So what is the correct observation?

2)what will happen if one frame is accelerating ie observer II.

 

[tiny-tim]

welcome to pf!

hi physicsManiac! welcome to pf!

1)if 2 identical charges move parallel to each other(along y axis) with relative velocity zero the the observer I moving along with the charges will observe force along one direction only(along x-axis electrostatic) whereas an observer II(standing at origin) watching the charges move away will observe a force on charges along both x and y direction(x and y-axis both i.e magnetic and electrostatic).So what is the correct observation?

if the speed is tanhα, then observer II measures the field as E_y = Ecoshα, B_z = Esinhα.

since the x component of velocity is tanhα, the total force (per unit charge) in the y direction is Ecoshα - Esinhαtanhα, = Esechα, which combined with time dilation gives us the same as the original E

(that still leaves a magnetic force in the x direction, which curves the path away from the "vertical" … but that's ok because for observer II the charges are not moving parallel to the y-axis, and the faster they move, the greater the angle to the y-axis )

2)what will happen if one frame is accelerating ie observer II.

uhh? why would anyone want to make calculations relative to an accelerating frame?

 

[kloptok]

So what is the correct observation?

I would say that both observations are equally correct. The same physics happens, just described in different ways.

Wasn't this essentially one of the thought experiments Einstein used to find the Lorentz transformation formulas by the way?