Use a boost along the wire axis when comparing frames. The current variable in a <four-current> must be <current density>, in $\mathrm{A\,m^{-2}}$, rather than a scalar total current in amperes. For the wire-force calculation it is convenient to integrate charge and current over each cross-section and work with line quantities.

Solution

Past exam of the optics and electrodynamics course of the University of Cambridge / 2018 / Section B / B4 / Solution

 Solution (source code)