Inductive Reactance of Solenoid with Solid Metal Core With respect to frequency

Inductive Reactance of Solenoid with Solid Metal Core With respect to frquency
Hi. Consider the Solenoid/Inductor Like one the Picture. There is Air gap between the coil and inserted solid metal.

Hi. Consider the Solenoid/Inductor Like one the Picture. There is Air gap between the coil and inserted solid metal. The solid metal is from Aluminum or Copper (Both have relative magnetic permeability , close to 1 regardless of temperature).

What will happen with inductive reactance of the given Solenoid if we increase the frequency of the applied voltage. Consider the Eddy currents. Thank you.

 
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The only magnetic force is due to eddy currents from velocity of the conductor with high DC current applied. It is viscous effect from resistive losses in the surface.

This can be seen with a strong rare earth magnet in a copper tube so the flux must be quite high to observe the same effect. Using AC won't move the metal and won't increase the winding current. Rather the current will decrease as the winding resistance increases with current and the induced EC load will be small but is used in HDD rotary voice coils with copper around the magnet to add a small amount of damping.
 
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