In Feynman Lectures on Physics vol 2 pg.13.6-13.10 develops the equations for a current carrying wire and a moving charge ( negative test charge) with the same velocity as the electrons in the current. He looks at this situation from two reference frames, 1) the wire still and test charge and electrons moving at velocity v and 2) the test charge and conduction electrons still and the wire with velocity -v.(adsbygoogle = window.adsbygoogle || []).push({});

Using relativity and the Lorentz factor gamma for reference frame 2), the test charge sees an electric field, while from rest frame 1) the test charge sees a magnetic field. Both reference frames result in the same change to the test charge's momentum toward the wire even though the two reference frame's forces (F_1,F_2) are different (i.e.F_2=F_1*gamma) because the relative delta in time (t_1=t_2*gamma) is opposite the delta in forces so momentums p_1=p_2 (p_1=F_1*t_1, p_2=F_2*t_2=F_1*gamma*t_1/gamma=F_1*t_1=p_1).

In http://en.wikipedia.org/wiki/Relativistic_electromagnetism the section "The origin of magnetic forces" has almost the same situation except the current is carried by positive charges and the test charge is positive (rather than negative current and negative charge). However wiki has both a Lorentz contraction for the negative charge and a Lorentz expansion of the positive charge resulting in the same electrostatic force (F_e) as magnetic force (F_m), i.e. F_e=F_m. Or in terms of Feynman's notation,F_2=F_1.

These two do not agree, which one is correct and why? Or if both are why?

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# Feynman's vs wiki's relativistic resultant

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