Question 2.39: Calculate the mutual inductance M between two small parallel...

The mutual inductance between the two loops is calculated using the definition of a mutual inductance $L_{12} \equiv M=\frac{\Lambda_{12}}{I_{1}} \approx \frac{N_{2} B_{1} s_{2}}{I_{1}}$. We use the results of Example 2-30 where the magnetic field on the axis from a small current carrying loop was calculated. Assuming that the separation distance is greater than the radius of either loop, we write $B _{1}=\frac{\mu_{0} N_{1} I _{1} s _{1}}{2 \pi d^{3}}$  . The mutual inductance is

$M \approx \frac{\mu_{0} N _{1} N _{2} s_{1} s_{2}}{2 \pi d ^{3}}$

The calculation of the mutual inductance is important in understanding transformers.