A small circular loop of radius a is placed inside a large square loop of edge `L(gt gta)` . The loops are coplanar and concentric. Find mutual inductance.

Explanation

To find the mutual inductance between a small circular loop of radius \( a \) and a large square loop of edge \( L \) (where \( L > a \)), we can follow these steps:

### Step 1: Understand the Configuration
We have a small circular loop of radius \( a \) placed inside a large square loop with edge length \( L \). Both loops are coplanar and concentric.

### Step 2: Determine the Magnetic Field Due to the Square Loop
The magnetic field \( B \) at the center of the square loop due to the current \( I \) flowing through it can be calculated. The magnetic field at the center of a square loop can be derived using the formula:

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