The resistance per unit length of a conducting wire is proportional to the square root of the ratio of permeability to conductivity. The power generated as heat may be expressed as I-squared x R: also as V-squared / R. In induction, the EMF induced is determined by the rate of change of the magnetic flux (Faraday). Thus, it would seem to me that the appropriate calculation of the heat produced in the conductor is given by V(induced) - squared / R. As a result, the heat is proportional to the square root of the ratio of conductivity to permeability (since R is in the denominator, above.) Thus, the higher the permeability (as in a ferromagnetic conductor) the lower the heat loss. This is contrary to the case where the current is constant, determined by an external source of EMF. In that case, the heat generated is proportional to the product of the current squared and the resistance: I - squared x R. In this case, the heat generated is proportional to the square root of the ratio of the permeability to the conductivity. In discussing why a high permeability is desirable in induction heating, the latter analysis is usually presented. But the induction current is not determined directly by an external source of EMF but instead by the changing magnetic flux from the primary current. It seems to me that the constant quantity is the induced EMF and not the induced current. Please help me understand why this is not correct.