Obtaining Maxwell's equations heuristically
  Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light together with Galileo invariance of the Lorentz force allows us to introduce arbitrary electrodynamic units naturally. 
Gerhard Diener, J\"urgen Weissbarth, Frank Grossmann and R\"udiger   Schmidt
physics.class-ph