This is a hard question i will be impressed if u can answer!
The general equation used for the design of electrical transformers is E4.44fNAB where E is in volts, f is in Hz, N is the number of turns, A is cross section of the magnetic path in sq.m and B is the induction in Tesla. B permeability of the magnetic core x H where H NI/l, I being current in ampere and l is the magnetic path length in meters. Once the magnetic core material is chosen, the maximum permissible B is decided upon to avoid saturation. Permeability is considered constant in the operating range of temperature and and current. Eddy current is considered to be contributing only to the rise in temperature of the core. What remains to be decided in the design is only to arrive at the values of A and N. The only conflict that I could see is that there is no direct or independent relation between the Power of the transformer, A and N. In practice, an empirical equation like Cross sectional area of the core ( cm^2) square root of P or 0.8x square root of P is used depending on the quality of the magnetic material chosen. Here P is in volt xampere. E is proportional to magnetic flux or rate of change of magnetic flux. But that is not enough to establish a power relation.
Wow eematers has a lot of information, but didnt answer the question. from mechanical design aspect, the electrical design is lighter, uses less expensive materials and is smaller. The magnetic design, to produce the equivalent voltage, would require large ferro-magnets (heavy, bulky) or equally strong rare-earth magnets which are more expensive. also the magnetic design is limited to cooler environments because of the curie point.(Temperature at whcih magnetic field is lost.
