For the first time, we report the critical dimension of the track width (wc=3 µm) to maximize the signal-noise ratio (SNR) of micro search-coil magnetometers (µSCM) through a synergy of theoretical scaling analysis and experimental study. A complete low-frequency model for sensitivity, noise, and SNR analysis is developed and validated by experimental results. Both the theoretical and experimental results indicate that the sensitivity of the sensor is proportional to $D_o^3$ (Do is the outer diameter of the spiral inductor), while the noise of the sensor is proportional to $D_o^1$ Besides, the experimental results indicate that the SNR of µSCM increases with $D_o^2$. The existence of a critical track width for fixed Do to achieve maximum SNR is proved both analytically and experimentally. Fabricated using a single mask, the µSCM with Do of 5mm achieves an SNR of 61.77dB at 50Hz frequency and 1 mT input magnetic field with 800Hz bandwidth. The proposed SNR- oriented design methodology and CMOS compatible fabrication process promise an accurate, reliable, and cost-effective solution for power monitoring IoT applications.