Magnetic levitation trains provide a high-speed, very low friction alternative to steel wheels on steel rails. The

Question:

Magnetic levitation trains provide a high-speed, very low friction alternative to steel wheels on steel rails. The train floats on an air gap as shown in Figure P2.27 [25]. The levitation force FL is controlled by the coil current i in the levitation coils and may be approximated by
FL = k i2/z2,
where z is the air gap. This force is opposed by the downward force F = mg. Determine the linearized relationship between the air gap z and the controlling current near the equilibrium condition.