We derive an equation that predicts the induced voltage across the receiving terminals of the three-coil head of a metal detector using a magnetic vector potential approach. We also derive an equation that relates the change of the impedance of the transmitting coil to the properties of the metal. We utilize the results to obtain the optimum spacing between the driving and the receiving coils at which the maximum induced voltage is attained. Further, we determine the position of the metallic object where the voltage reaches its peak. We verify our work by comparing the results with those of a previous work