Two circular coils, one of smaller radius `r_(1)` and the other of very large radius `r_(2)` are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.

Explanation

To find the mutual inductance \( M \) of two coaxial circular coils, one with a smaller radius \( r_1 \) and the other with a very large radius \( r_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
- Let \( n_1 \) be the number of turns per unit length of the inner coil (radius \( r_1 \)).
- Let \( n_2 \) be the number of turns per unit length of the outer coil (radius \( r_2 \)).
- Let \( L \) be the length of both coils.
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