From: ram@zedat.fu-berlin.de   
      
   ram@zedat.fu-berlin.de (Stefan Ram) wrote or quoted:   
   >The back-reaction of the second coil on the power follows from Ohm's   
   >law and Maxwell's equations, but not from Faraday's law alone.   
      
     It may be instructive to say that Maxwell's laws   
      
   Gauss's law (electricity): div E = rho / epsilon_0   
      
   Gauss's law (magnetism): div B = 0   
      
   Faraday's law: curl E = - dB/dt   
      
   Ampere-Maxwell law: curl B = mu_0 J + mu_0 epsilon_0 dE/dt   
      
     can be written as just   
      
   d F = 0, d *F = J   
      
     after E and B are united to the two-form F (d being the exterior   
     differential, * the Hodge dual, and J the current 3-Form).   
      
     Even if one is not familiar with the exterior differential, this   
     show the unity of Maxwell's equations. They are just one single   
     law. So, this might make it clear that while "Faray's law" was   
     found before Maxwell's equations historically, one cannot actually   
     just split Faraday's law away and consider it in isolation always.   
      
     (I'm kinda tempted to define an operator "D" as the pairing   
     (d,d*) and a pairing j as (0,J) and then write "DF=j". Well,   
     you can see it this way, but that's my non-standard notation.)   
      
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