Analytical Solutions of Electromagnetic Fields from Current Dipole Moment on Spherical Conductor in a Low-Frequency Approximation

Abstract

We analytically derive the solutions for electromagnetic fields of electric current dipole moment, which is placed in the exterior of the spherical homogeneous conductor, and is pointed along the radial direction. The dipole moment is driven in the low frequency f = 1 kHz and high frequency f = 1 GHz regimes. The electrical properties of the conductor are appropriately chosen in each frequency. Electromagnetic fields are rigorously formulated at an arbitrary point in a spherical geometry, in which the magnetic vector potential is straightforwardly given by the Biot–Savart formula, and the scalar potential is expanded with the Legendre polynomials, taking into account the appropriate boundary conditions at the spherical surface of the conductor. The induced electric fields are numerically calculated along the several paths in the low and high frequeny excitation. The self-consistent solutions obtained in this work will be of much importance in a wide region of electromagnetic induction problems.