From: ralivingston1952@charter.net   
      
   There are actually two ways to do EM: by electric and magnetic fields   
   using Maxwell's equationa or by summing the electromagnetic 4-potential   
   (with Lorentz transforms for moving charges) for all charges in the   
   system (both free and bound).  The former approach involves working with   
   a 2nd rank EM field tensor while the latter involves only a single rand   
   tensor (a 4-vector).   
      
   The brilliant thing about the Maxwell approach is that you don't have to   
   know the distribution and motions of the bound charges (in dielectrics   
   and metals) as you can use simple boundary conditions to get approximate   
   solutions that are quite good in almost all practical cases.  The   
   4-potential approach requires you to solve for all the bound charge   
   densities and motions, which you can't do without knowing the fields,   
   which you can't know without knowing the bound charge distributions...   
   This is not a problem in principle, but is a big problem for practical   
   calculations.   
      
   Rich L.   
      
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