Measurement of mutual inductance from frequency dependence of impedance of AC coupled circuit using digital dual-phase lock-in amplifier

We present a simple method to determine the mutual inductance M between two coils in a coupled AC circuit by using a digital dual-phase lock-in amplifier. The frequency dependence of the real and imaginary part is measured as the coupling constant is changed. The mutual inductance (M = kL) decreases with increasing the distance d between the centers of coils. We show that the coupling constant is proportional to d^{-n} with an exponent n (\approx 3). When the current flows in the coils, the coil is magnetically regarded as the magnetic moment. The physics of the mutual inductance is similar to that of two magnetic moments coupled by a dipole-dipole interaction