An analytical formula of induced electric field E in a spherical conductor by an ELF dipole magnetic field source M = M∥ + M ⊥ is mathematically derived in vector form based on the equivalent multipole moment method with re-expansion technique (RE-EMMM), where M∥ and M⊥ are parallel and perpendicular components of M, respectively. The validity of the formula is confirmed by the following three ways. (i)The derivation of the formula from the Sarvas equation with the reciprocity theorem derived by Eaton. (ii)The convergence of the formula to that of homogeneous magnetic field when M∥ is located at the infinite distance, (iii)Comparison of the analytical solutions with numerical solutions by RE-EMMM. Furthermore, an formula for the trajectory, which satisfies E = 0, is derived for the field by M∥.