The eddy-currents that are induced in a thin conducting sheet by a sinusoidally varying primary magnetic field are investigated in the low frequency limit, when the depth of penetration of the· primary field is much greater than the thickness of the sheet, by setting up a perturbation scheme in terms of the small parameter, $\delta$, which is the ratio of the thickness of the sheet to the length scale of the primary field. The terms of zero order in $\delta$ give the familiar results that were first obtained by Maxwell. The terms of first order in S depend on the tangential as well as the normal component of the primary field and give eddy-current distributions that vary quadratically across the sheet. The boundary conditions that determine the accompanying secondary magnetic field are derived. Detailed results are given when the primary field is that due to a dipole.
The results are relevant to problems in ionospheric physics and geophysical exploration.