Electric field in different frames of reference

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SUMMARY

The discussion centers on the behavior of electric fields in different frames of reference as described by special relativity. A point charge +q moving along the x-axis with velocity v generates different electric field values when calculated from the stationary frame S and the moving frame S'. The participant correctly applies the electric field equation E=q/x² in frame S and finds E'=q/(γ*x)² in frame S', but encounters confusion regarding the expected equivalence of the results. The discrepancy arises from the application of Lorentz transformations and the nature of electric fields in relativistic contexts.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with electric field equations for point charges
  • Knowledge of Lorentz transformations
  • Basic concepts of electromagnetism
NEXT STEPS
  • Study the electromagnetic tensor and its role in special relativity
  • Learn about the implications of Lorentz transformations on electric and magnetic fields
  • Explore the concept of relativistic electric fields in different inertial frames
  • Investigate the relationship between electric fields and charge motion in relativistic contexts
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Students of electromagnetism, physicists studying special relativity, and educators seeking to clarify the relationship between electric fields and frames of reference.

tamir
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I study electromagnetism and I got to the chapter about special relativity, in this chapter my professor (since we are not using the electromagnetic tensor in this course) used a specific case to show that the electric field parallel to the velocity of a frame of reference stay the same in both the original frame and the moving frame.

However when I look at the given situation of a point charge +q moving in the x-axis with velocity v, relative to a frame called S, and I calculate the electric field in both the S frame and in the point charge frame (S'), I get different values for the electric field in each frame.

Say the particle cross the origin of the S frame at t=0 at the S frame, and at t'=0 in his frame, and we want to calculate the field he generates at (x,0,0) (coordinates of S), what I have done is:
In the S frame I used the regular equation of the electric field of a point charge E=q/x^2 and in the S' frame I also used this equation E'=q/x'^2 and used lorentz transformation and got E'=q/(γ*x)^2.
Other students told me I should have got q/(γ*x)^2 in both frames and from some reason I can't calculate the electric field of the charge in the frame he moving in using E=q/r^2, but I don't know why.
 
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