How Does Relative Motion Affect Magnetic and Electric Forces on a Charge?

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SUMMARY

The discussion focuses on the effects of relative motion on electric and magnetic forces acting on a charge, particularly in different reference frames. In frame S, the electric force is zero, while in frame S', the electric force is non-zero due to the presence of charges. The magnetic force in frame S' arises from the movement of positive charges and is calculated using Ampère's Law. The key question is whether the magnetic force will counterbalance the electric force in the new frame, necessitating the application of Gauss's Law to find the electric field and Lorentz contraction to analyze the distances between charges.

PREREQUISITES
  • Understanding of Gauss's Law for electric fields
  • Familiarity with Ampère's Law for magnetic fields
  • Knowledge of Lorentz contraction in special relativity
  • Basic concepts of electric and magnetic forces
NEXT STEPS
  • Study Gauss's Law to calculate electric fields in various reference frames
  • Learn about Ampère's Law and its application to moving charges
  • Research Lorentz contraction and its implications for electric and magnetic forces
  • Explore the relationship between electric and magnetic fields in special relativity
USEFUL FOR

Students and professionals in physics, particularly those studying electromagnetism and special relativity, will benefit from this discussion. It is also relevant for educators looking to explain the interplay between electric and magnetic forces in different reference frames.

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http://higgs.phys.washington.edu/phy121b/HW/light speed changes.pdf

Above is what I need to do. So essentially, I have to show that in the new reference frame, that the new magnetic force will counter the old electric force. So then I have to use the equation of attraction due to a wire, and then some lorentz contraction. buit then i think I'm lost...Thanks!
 
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So, in the new frame, are the + charges closer together or farther apart?
Are the - charges closer together or farther apart?

The "old" Electric Force was zero, as measured in frame S.
The electric Force in frame S' is not zero. (recall Gauss to find E).
The magnetic Force due to the (moving) + charges in frame S' is not zero.
(recall Ampere to find B).
Do they cancel?
 

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