Find mutual inductance if we have a square loop of side r instead of a small circular loop of side r at the centre of bigger circular loop.

Explanation

To find the mutual inductance \( M \) when a square loop of side \( r \) is placed at the center of a larger circular loop of radius \( R \), we can follow these steps:

### Step 1: Understand the Configuration
We have a larger circular loop with radius \( R \) carrying a current \( I \). At the center of this loop, we place a square loop with side \( r \).

### Step 2: Determine the Magnetic Field at the Center of the Circular Loop
The magnetic field \( B \) at the center of a circular loop carrying current \( I \) is given by the formula:
\[
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