The broad survey of alternate formulations of Maxwell's Law <http://en.wikipedia.org/wiki/Maxwell%27s_equations#Alternative_formulations> (which I use in preference to "Maxwell's Equation(s)") shows an interesting pattern:
In every non-homogeneous formulation, the right hand side shows some expression of the current field times the permeability of free space. Moreover, most of the left hand sides involve the magnetic vector potential. Both sides of these equations have the same physical dimensions as the magnetic vector potential. By inverting the dimensions of both sides, one may express the critical physical dimension of Maxwell's Law as: velocity per electric potential This has intuitive meaning worth contemplating. Derivation: The vector potential has dimension: momentum per charge In cgs units (gramm = gram as mass as opposed to force in one gravity): gramm*cm/(s*coulomb) The permiability of free space <http://en.wikipedia.org/wiki/Vacuum_permeability> times current has dimension: current electric potential time per (current length) In cgs units: amps*volts*sec/(amps*cm) The amps cancel: volts*sec/cm Subjecting the two sides to a dimensional analysis calculator <http://www.testardi.com/rich/calchemy2/>: gramm*cm/(s*coulomb)?volt*s/cm (gramm * [centi*meter]) / (second * coulomb) ? (volt * second) / (centi*meter) = 1E-7 volt*s/cm In other words, the dimensions of these two units-based expressions match, with only a constant of proportionality difference. Examining the right hand side, the not-so-intuitive ratio "s/cm" has the inverse dimension of velocity, so we can reconsider Maxwell's Law reformulated in terms of a left hand side which is the inverse of the vector potential, and the right hand side which is: (s*coulomb)/(gramm*cm)?(cm/s)/volt (second * coulomb) / (gramm * [centi*meter]) ? ([centi*meter] / second) / volt = 1E7 (cm/s)/volt So we see (cm/s)/volt or velocity per electric potential is not only a relatively intuitive dimension -- it is central to formulations of Maxwell's Law.
