HIGH FREQUENCY ELECTROMAGNETS

The force between two magnets equals B²A/(2KU₀)

where:

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.

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