The force between two magnets equals B2A/(2KU0)
B is the magnetic field (measured in teslas),
A is the cross-sectional area (in square meters),
K is the relative permeability of the magnet (non-dimensional),
U0 is the permeability of vacuum (4(PI)E-7 henry per meter).

Electromagnets operating at a low frequency are efficient, because they can use soft magnetic materials having a high saturation induction. For example, a transformer operating at 60 Hz can use alloys having a saturation induction of 2 teslas and almost no core loss.

Electromagnets operating at a frequency of 1 MHz must use high-frequency ferrites (Mn-Zn or Ni-Zn), which have a saturation induction of only 0.33 tesla. The high-frequency ferrites are (2 / 0.33)2 times heavier than the low-frequency alloys. Furthermore, electric insulation of the high-frequency electromagnets is thick and heavy.

Superconductive electromagnets, transformers, motors, and generators exist, but they melt down when the magnetic field change rate exceeds several teslas per second. A linear motor accelerating cargo to the orbital velocity experiences a magnetic field change rate of millions T/s.


H. Nakamura, H. Matsumoto, H. Hasegawa, K. Nakanishi, K. Inoue, and M. Sakai, "Static Excitation Test Results of the Partial Rotor Model for 70 MW Class Superconducting Generator with Quick Response Excitation," IEEE Transactions on Magnetics, Vol. 32, No. 4, July 1996, pp. 2357-2360.