Frequency series expansion of an explicit solution for a dipole inside a conducting sphere at low frequency

The electromagnetic field generated by a current dipole situated at an arbitrary position inside a conducting sphere is derived using the expansions of the spherical vector wave functions. The first few terms in a series expansion of this field with respect to the frequency are given for the normal magnetic field (used in magnetoencephalogram) and the tangential electric field (used in electroencephalogram) outside the conducting sphere at low frequency. It is shown that the first correction term to the static solution is linear in the frequency ω (the second correction term is proportional to ω ³2/) and, thus, the static solution can be used as a good approximation for the solution at a very low frequency.