Usually power generating synchronous generators are rated at around 85-90% efficiency. Curiosity struck me as of how a generator with field coils can ever go to such an high efficiency.
My thought process is as follows.
The power balance for the considered generator with permanent magnets are first considered 2N* 1 ms-1 and 2W generated power match in this case
Now imagine the 1T permanent magnet has now been replaced with electro magnet. In order to get one Tesla magnetic flux density according to the Ampere's law it takes ~500000 A on a 0.1 m conductor.
Obviously this doesn't add up and something is incorrect in my thinking. Appreciate it if someone can point what is wrongs in the above and show me how to calculate the correct excitation current on the field coils.