## 1 Introduction
### Physical Background of the Method
The presence of active resistance \(R\) and reactive capacitive resistance \(X_{C}\) results in an additional (compared to \(\pi/2\) in the perfect coil) phase shift \(\varphi_{L}\) (loss angle), which thus characterizes the energy loss in the coil on \(R_{\Omega}\) and \(R_{C}\) resistances [16; 17]. The losses in the coil are usually characterized by a loss angle tangent (\(tg\varphi_{L}\)) and its reciprocal value, which is called the quality factor \(Q\). When determining the quality factor, all resistances related to losses are combined in the loss resistance \(R_{L}\):  
\[Q=\frac{X_{L}}{R_{L}}=\frac{1}{tg\varphi_{L}}, \tag{5}\]  
where, in the case of core presence, \(R_{L}\) can be generally written as  
\[R_{L}=R_{\Omega}+R_{C}+R_{core} \tag{6}\]  
where \(R_{\Omega}\) is the ohmic resistance, \(R_{C}\) is the capacitive resistance, and \(R_{core}\) is the resistance corresponding to the losses in a core. The \(R_{\Omega}\) and \(R_{C}\) resistances describe the losses directly in the coil and material of its frame respectively, and the resistance \(R_{core}\) corresponds to the losses in the core material. Losses in a conductor (wire) are described by active (ohmic) resistance, which can be calculated according to the following equation:  
\[R_{\Omega 0}=\rho\frac{l}{S}=\frac{4l}{\pi d^{2}}\rho, \tag{7}\]  
where \(l\) is the length of the wire, \(d\) is the diameter of the wire, \(\rho\) is the resistivity, and \(S\) is the cross-sectional area of the wire. Therefore, the ohmic (active) losses in the conductor can be considered if the parameters of the coil and its windings are known. The capacitive resistance of the \(R_{C}\) explains the losses in the conductor insulation material and in the coil body. The resistance of \(R_{core}\) can be represented as the sum of \(R_{ed}\) corresponding to eddy current losses, and \(R_{M}\) corresponding to losses of magnetic nature. \(R_{al}\), eddy currents (Foucault currents), are induced in the core of the material coil by the alternating electromagnetic field generated by the coil. These currents contribute to losses due to their dissipation in the core. \(R_{M}\) corresponds to the loss of the magnetic nature caused by the hysteresis phenomenon. Thus, on the basis of the aforementioned, information about the magnetic state of the coil's core can be obtained from the inductance of the coil, and it is also possible to separate the characteristics of the coil itself from the characteristics of the material being measured. Conclusions about the mass, density, and surface area of the magnetic material can be drawn from the measurement of the specified parameters of the car with a load as its core. The morphology of the load, the anisotropy of its characteristics, and its spatial and magnetic orientation can also be determined [15]. If a magnetic measurement to estimate the mass of a magnetic object occurs after measurement on a railway scale, then conclusions on the mass, density, and surface area of the magnetic material can be made from measurements of the indicated parameters of the coil with a load as its core. Non-magnetic materials including earth, concrete, polymers, and others, do not affect the magnetic signal, but significantly change the weight of the car with the load. This pattern underlies the operation of the device. The methods used for determining and accounting for the spatial morphology and magnetic orientation were analyzed in this study and applied in a real-life sample.