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

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Relative motion significantly impacts the electric and magnetic forces experienced by a charge. In the original reference frame (S), the electric force is zero, but in the new frame (S'), it becomes non-zero due to the presence of moving charges. The magnetic force, generated by these moving positive charges, also contributes to the overall force in frame S'. The discussion revolves around whether the electric and magnetic forces in the new frame cancel each other out. Understanding the spatial arrangement of charges and applying relevant equations, such as those from Gauss and Ampere, is crucial for resolving these forces.
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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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