Dependence of damping constant on current

[PlickPlock]

Using an eddy current brake, one would expect the damping constant ##δ## to increase with the current ##I## supplied to the eddy current brake. My question is, why is ##δ## proportional to ##I^2## and not merely ##I##?

The magnitude of the eddy current is ##\frac{1}{R}\frac{dΦ}{dt}##, which is why I initially thought ##δ## was proportional to ##I##, because the induced current is proportional to ##\frac{dΦ}{dt}##.

P.S: This link http://home.uni-leipzig.de/prakphys/pdf/VersucheIPSP/Mechanics/M-17E-AUF.pdf
was what I used as reference; it stated the relation but does not seem to explain why.

 

[Hesch]

why is δ proportional to I² and not merely I?

The B₁-field induced by the brake is proportional to I.
The induced eddy voltage in the disk is proportional to the B₁-field.
The induced eddy current in the disk is proportional to the eddy voltage.
The induced B₂-field from the disk is proportional to the eddy current.
The braking force is proportional to the magnetic energy density in the airgap = ½*B₁*(B₂/μ₀) [ J/m³ ].

That's why.