Electromagnetic Induction in Thin Finite Sheets having Conductivity Decreasing to Zero at the Edge, with Geomagnetic Applications I

Electromagnetic induction in thin sheets in the forms of a circular disk, an infinite strip of uniform width and a hemispherical shell is considered theoretically with view of investigating the coastline effects on geomagnetic variations. The distribution of conductivity over the surface of each sheet is such that it decreases to zero at the boundary. In the geomagnetic application, the sheet represents a large ocean. The results show that for a uniform (or dipole) inducing field, the vertical component is enhanced in sea and land near the coastline where it reaches its maximum. In sea at the region where the depth of the ocean begins to decrease (the continental shelf), the induced vertical component is reversed and the horizontal component attains its maximum. For a large ocean, these effects should be observable for periods of up to 24 hours. In case of sudden changes, the effects should last more than an hour before decaying.