Final answer:
Mutual inductance is a geometric property relating to the shape and positioning of wire loops, and for a small loop within a larger one with overlapping centers, it is proportional to the larger loop's side squared divided by the smaller loop's side.
Step-by-step explanation:
The mutual inductance of two loops is a property that quantifies the extent to which a change in electric current in one loop induces an electromotive force (emf) in a second loop. According to the question, we have a small square loop of wire with side l, placed inside a larger square loop of wire with side L (where L is much greater than l). The mutual inductance (M) in such a configuration is dependent on the geometry of the two loops.
While the exact calculation for mutual inductance can be complex due to the intricacies of magnetic fields, mutual inductance is fundamentally a geometric quantity. It relies on the shapes and relative positioning of the loops. Since the large loop L has a much greater side length compared to the small loop l and they share a common center, the mutual inductance is proportional to the square of the large loop side divided by the small loop side, which can be mathematically expressed as M ∝ L²/l.
Mutual inductance is an important concept in the study of electromagnetic fields and has practical implications in the design of electrical circuits and components such as transformers and inductors.