Question 2.39: Calculate the mutual inductance M between two small parallel...
Calculate the mutual inductance M between two small parallel circular loops that have surface areas s1 and s2 that are separated by a large distance d. There are N1 turns that have a current I1 in the first loop and N2 turns in the second loop. The dashed lines indicate the magnetic flux density which is assumed to be approximately constant inside the loops.
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.