Analytical Formula of Induced Electric Fields in a Spherical Conductor by an ELF Dipole Magnetic Field Source

An analytical formula of induced electric field E in a spherical Conductor by an ELF dipole magnetic field Source M = M(parallel to) + M(perpendicular to) is mathematically derived in vector form based on the equivalent mutlipole moment method with reexpansion technique (RE-EMMM), whereM(parallel to) and M(perpendicular to). are parallel and perpendicular components of M, respectively. The validity of the formula is confirmed in the following three ways: (i) the derivation of the formula front the Sarvas equation with the reciprocity theorem derived by Eaton; (ii) the convergence of the formula to that of homogeneous magnetic field when M(parallel to) is located at the infinite distance; (iii) comparison of the analytical Solutions with numerical solutions by RE-EMMM. Furthermore, it formula for the trajectory, which satisfies E = 0, is derived for the field by M(parallel to). (C) 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(3): 8-17, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eeej.20739