  This paper describes an analytical evaluation of the quality factor Qz in a
separable system in which the vector potential is known. The proposed method
uses a potential definition of active and reactive power, implicitly avoiding
infinite entire space integration and extraction of radiation energy. As a
result, all the used quantities are finite, and the calculated Qz is always
non-negative function of frequency. The theory is presented on the canonical
example of the currents flowing on a spherical shell. The Qz for the dominant
spherical TM and TE mode and their linear combination are found in closed
forms, including both internal and external energies. The proposed analytical
method and its results are compared to previously published limits of the
quality factor Q.
