In all probability the only way to understand the theoretical possibilitiesand limitations of magnetic analysis is the use of a trial-and-error method.To demonstrate this, a virgin field of rigorous mathematical foundations of athree-dimensional (3D) equilibrium problem is briefly presented. In the firstpart of the paper we clarify the problem of plasma profile determination. Wepreviously have established the limitations following from a direct 3D plasmaequilibrium problem on the possibility of the moderate current density profileidentification. Here we demonstrate the limitations on the pressure profiledetermination under zero net current regime of operation. Realisticexperimental conditions that significantly complicate the use of magneticanalysis for equilibrium identification are outlined. The second part of thepaper deals with the peculiarities of diamagnetic measurements instellarators. The influence of the 3D plasma induced magnetic fields isbriefly sketched. We will also treat in detail an attractive, althoughquestionable, possibility for the estimation of the electron cyclotronresonance heating absorbed power from the jump in the time derivative of thediamagnetic signal. It is shown that the limitations of such a method arecompletely determined by the accuracy of the experimental system set-up, butdo not depend on the mathematical properties of the equations considered, aswas previously expected.