Hi, the attached picture should show Griffiths derivation of the flux rule for motional emf. To refresh your memory it says that minus the rate of change of the magnetic flux equals the emf: -d[itex]\Phi[/itex]/dt = [itex]\epsilon[/itex] Now, I need some help in understanding the attached derivation. Griffiths starts by saying that the flux rule actually works for arbitrarily shaped current loops in non-uniform magnetic fields and even if the surface of the loop changes shape(*). I am however unsure in which of these he actually sets out to prove. Since he calculates the flux for a surface S and the same surface deformed, I would say he tries to prove (*) - is that correct? And if so, are the two other properties also proven or are they simply something left for the rigorous mathematicians?