Relativistic moment of a particle

Relativistic moment of a particle. See attached file for full problem description.

Force between electrons moving side by side

calculate the force, a observed in the laboratory, between two electrons moving side by side along parallel paths 1 millimeter apart if each has a kinetic energy of (a) 1 electronvolt and (b) 1 megaelectronvolt

Electromagnetics

Show that B^2 - E^2 / c^2 is invariant under a Lorentz transformation.

Relativity/time-independent magnetic field

Assume that, in S, there is a constant magnetic field and no electric field. Show that E' = V cross B' in S'. Note the prime on the right hand side. So E' is perpendicular to V and B'.

Time Elapsed on a Clock

Time Elapsed on a Clock. See attached file for full problem description.