From: PointedEars@web.de   
      
   Kuan Peng wrote:   
   > Le 21/01/2026 à 22:20, ram@zedat.fu-berlin.de (Stefan Ram) a écrit :   
   >> Kuan Peng  wrote or quoted:   
   >>> Great. But Faraday’s law does not specify how much more energy than   
   >>> without the other coil.   
      
   Gibberish.   
      
   >> This is the missing term of Faraday’s law.   
   >>   
   >>   Faraday's law states that a time-varying magnetic field induces   
   >>   a circling electric field.   
   >>   
   >>   It does not give that energy.   
   >>   
   >>   But that does not mean that terms need to be added to Faraday's   
   >>   law because Faraday's law is not meant to describe everything   
   >>   in the world when it is taken in isolation.   
   >>   
   >>   That energy? It can be calculated using a combination of several laws.   
   >>   
   >>   Faraday's law gives the induced emf E2(t) in the second loop from the   
   >>   time rate of change of magnetic flux due to the first coil's current.   
   >>   
   >>   E2(t) = - M * dI1/dt   
   >>   
   >>   where M is the mutual inductance and I1(t) is the current in the   
   >>   first coil.   
   >>   
   >>   With the loop 2 resistance R known, Ohm's law gives the induced   
   >>   current   
   >   
   > I see. Faraday’s law is a tool.   
      
   No, Faraday's law _of induction_ (how many more times do I have to tell   
   you?) is an empirically confirmed physical law.   
      
   AISB, you could not read this if it were fundamentally wrong: most electric   
   appliances, certainly electronic devices, include transformers (or require   
   power adapters which include them to transform high voltage to low voltage)   
   which are working based on that law:   
      
      
      
   > As a tool, it does not have to respect the law of conservation of energy   
      
   No, you simply have no clue what you are talking about.   
      
   > Poynting’ theorem is a tool and does not have to respect the law of   
   > conservation of energy   
      
   No, you simply have no clue what you are talking about.   
      
   > Ohm's law is a tool and does not have to respect the law of conservation   
   > of energy   
      
   No, you simply have no clue what you are talking about.   
      
   > We have to combine several laws to fabricate a global solution that   
   > respects the law of conservation of energy   
      
   No; as I have proved to you in the very beginning, when we calculate the   
   change of the energy density of the electromagnetic field with respect to   
   time, the continuity equation for (classical) electrodynamics including   
   the Poynting vector and the work done by the elctromagnetic field, results   
   *naturally*.   
      
   What I have not shown is how to calculate the energy density itself because   
   it is a rather lengthy calculation.  But it can be shown by integrating the   
   Lorentz force   
      
     F = q (E + V × B)   
      
   over the path of a charged particle, which in turn can be derived from the   
   special-relativistic (Lorentz-covariant) Lagrangian for a charged particle   
   coupled to the electromagnetic field (given by the Maxwell tensor with   
   components F_ab = ∂_a A_b − ∂_b A_a, where A_a = [−ϕ/c, A] is the   
   four-potential, where ϕ is the electric potential in E = −∇ϕ, and A is   
   the   
   magnetic vector potential in B = ∇ × A).   
      
   --   
   PointedEars   
      
   Twitter: @PointedEars2   
   Please do not cc me. / Bitte keine Kopien per E-Mail.   
      
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