Metal detectors are extensively used to find undesirable metal objects in processed food. In such a typical metal detector, the coils are coaxially arranged with the transmitting coil in the center and two receiving coils on the sides. The receiving coils are connected to a differential amplifier. When the magnetic field generated in the transmitting coil is disturbed by metal objects, the amplitude and phase of the output voltage of the differential amplifier change, and, thus, the existence of foreign metal pieces is detected. The relationship between the amplitude and phase of the output and the electromagnetic properties of the metal objects, however, has only been discussed experimentally so far. The authors have already developed the SRPM method to simultaneously estimate the electrical and magnetic properties of a spherical sample by vectorially measuring the difference in the impedance of two circular solenoid coils, one with and the other without a sample. An attempt is made to theoretically analyze the properties, such as size, conductivity, and permeability of the metal objects from the output, i.e., amplitude and phase of the metal detector. Based on this method, an equation to estimate the vector voltage induced in the receiving coil by the metal object is derived by using a spherical sample to simplify the analysis.