From: ram@zedat.fu-berlin.de   
      
   Kuan Peng  wrote or quoted:   
   >Great. But Faraday’s law does not specify how much more energy than   
   >without the other coil. 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   
      
     I2(t) = E2(t) / R.   
      
     The power dissipated as heat in the second loop is then   
      
     P2(t) = E2(t) * I2(t) = [E2(t)]^2 / R   
      
     The extra energy delivered to the second loop over some time   
     interval [t0, t1] is   
      
     W2 = integral from t0 to t1 of P2(t) dt   
        = integral from t0 to t1 of [E2(t)]^2 / R dt   
      
     Thus, Faraday's law provides E2(t); combined with the known   
     resistance R (and, if needed, the mutual inductance M and   
     primary current I1(t)), it determines the additional power   
     and energy absorbed in the second coil, without adding any   
     new term to Faraday's law itself.   
      
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