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Open Access Publications from the University of California

Parametric forms and the inductive response of a permeable conducting sphere

  • Author(s): Smith, J. Torquil
  • Morrison, H. Frank
  • Becker, Alex
  • et al.

At early time, the time derivative of the response of isolated conductive bodies to step function excitation decays as t-1/2 (under a quasi-static approximation). One simple parametric form for the response with correct early time behaviour is k'(1 + t1/2/a1/2)-beta e-t/gamma. For a conducting magnetic sphere, parameter values are determined from the high and low frequency limit responses, together with two time scales taken from the form of the analytic solution. Parameters alpha and gamma correspond to transition times, for transition from an early time t-1/2 derivative response, and to late time exponential decay. For conducting spheres with high permeability, increasing the permeability moves the transition from early time behaviour earlier in inverse proportion to the relative permeability mu r, and increases the time constant of the late time decay in proportion to mu r. Magnitude parameter k' corresponds to the difference between high frequency and low frequency limit responses.

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