Question

A small conducting square loop of side \( l \) is placed inside a concentric large conducting square loop of side \( L \) (where \( L \gg l \)). The value of mutual inductance of the system is expressed as \( \frac{\mu_0 l^2}{\pi L} \). The value of \( n \) is ............ (Round off to two decimal places).

Hint:

In cases where \( L \gg l \), the mutual inductance \( M \) is inversely proportional to \( L \), meaning a larger separation reduces the mutual coupling.

Answer 1

Correct Answer: 2.8

The mutual inductance \( M \) between two coils is given by \[ M = \frac{\mu_0 l^2}{\pi L}. \] This expression for mutual inductance shows the relationship between the mutual inductance and the geometry of the loops. If \( L \gg l \), the mutual inductance depends on the ratio \( \frac{l^2}{L} \). The value of \( n \) can be obtained from this ratio: \[ n = \frac{\mu_0 l^2}{\pi L}. \] Final Answer: The value of \( n \) is obtained by substituting the given values for \( l \) and \( L \).