Some Results on the Magnetic Field of Electric Currents Induced in a Thin Hemispherical Shell of Finite Conductivity, with Geomagnetic Applications

We consider the induction of electric currents in a thin uniformly conducting hemispherical shell by axisymmetric time-varying fields. A method of successive approximation to the solution is developed; the first approximation corresponds to the perfectly conducting shell. Using the vector potential of the fields, the first and second approximations are obtained for certain external fields. The results for the first approximation agree with those obtained by Ashour using the scalar potential. However, the analysis given here is simpler. The results are applied to electromagnetic induction in a large ocean and to the effect of the concentration of the induced currents near the edge. For variations of periods up to 24 h, the second approximation is found adequate. The calculations made for a varying field of 24 h period show that the vertical component of the induced field is enhanced near the coastline in both sea and land, and is reversed in direction on crossing the coast. The horizontal (tangential) component of the field is enhanced near the edge in the sea.