Kevin Zhou — Advanced Relativity Problem 3 · Kevin Zhou #R3.3
Physics · modern-physics · relativity
Problem
Problem 2(Purcell5.29). Twoprotonsaremovingantiparalleltoeachother, alonglinesseparated
by a distance r, with the same speed v in the lab frame, as shown.
Consider the moment the protons are a distance r apart.
(a) Show that the three-force experienced by each proton due to the electric field of the other is
γe2
F = .
4πϵ r2
0
(b) Compute the three-force experienced by one of the protons by transforming to its rest frame,
computing the force there, then transforming back to the lab frame. In particular, show that
this is not equal to the result of part (a).
(c) Show that the discrepancy is resolved if the magnetic three-force is also included.
Recall from R2 that the Lorentz three-force is F = q(E+v×B). You will also have to use the
three-force transformation laws you derived there.