Solving Magnetic Field Force: Observer I vs Observer II

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SUMMARY

The discussion centers on the observations of two identical charges moving parallel to each other along the y-axis, analyzed from two different reference frames: Observer I, who moves with the charges, and Observer II, who remains stationary at the origin. Observer I perceives only an electrostatic force along the x-axis, while Observer II detects both magnetic and electrostatic forces acting along the x and y axes due to the motion of the charges. The analysis reveals that the forces observed by both observers are valid within their respective frames, highlighting the relativity of observations in electromagnetic contexts. The discussion also references the Lorentz transformation, suggesting its foundational role in understanding these phenomena.

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physicsManiac
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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.
 
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welcome to pf!

hi physicsManiac! welcome to pf! :smile:
physicsManiac said:
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 Ey = Ecoshα, Bz = 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 :smile:

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

uhh? :redface: why would anyone want to make calculations relative to an accelerating frame? :confused:
 
physicsManiac said:
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?
 

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