Magnetic flux as affected by eddy currents in electromagnets

A method has been developed for determining the current time constant τ at which eddy currents become detrimental to electromagnet operation. Plots of flux density
B
versus time, and current
I
versus time were made for various values of τ on electromagnets having a constant air gap and a fixed value of maximum current I
m
in the coil. Such an electromagnet can be approximated by a linear
RL
circuit as long as eddy current effects are negligible. τ was the time required for the current to reach 0.63 I
m
. This corresponds to the time constant in a linear
RL
circuit. Values of
dB/dt
were measured at τ and the relationship
dB/dt = C/\tau^{m}
, where
m
equals 1 and
C
is a constant, was found to be applicable for large values of τ, as expected in a linear
RL
circuit. The τ value τ
c
at which
m
began to decrease from 1, determined the onset of eddy current effects since the circuit is no longer linear. Experimental results were compared to a theoretical solution for a ramp field applied to sheets of thickness δ. Calculations were performed of the time
\Deltat
by which the flux density lags the applied field. Reasonably good correlation was obtained between
\Deltat
and τ
c
. Measurements were made on various soft magnetic materials in various thicknesses. The results provide a guide in selecting material and lamination thickness for a given application.