The transient electromagnetic field of a permeable and conducting hollow sphere excited by a loop of arbitrary shape

The calculation of the transient electromagnetic field in solid conductors becomes more important in the future because of the increasing demands on system design under EMC-constraints. In this paper an analytical solution for the transient current distribution in a permeable and conducting hollow sphere is given for an exciting current of arbitrary time dependence that flows in a loop of arbitrary shape. The solution describes the shielding of the transient electromagnetic field in a very general form in case the exciting loop or an exciting dipole is located inside or outside the hollow sphere. Moreover, it can serve as a reference solution for a comparison with the results of numerical methods. For those methods it is known that the very fine discretization of thin screens becomes cumbersome. This difficulty increases for the calculation of transient fields because the transient current distribution becomes singular on the surface of conducting screens at the transition of a switching process. Copyright © 1999 John Wiley and Sons, Ltd.