Two insulated wires are wound on the same hollow cylinder so as to form two solenoids sharing a common air-filled core. Let `l` be the length of the core, `A` the cross -sectional area of the core, `N_(1)` the number of times the first wire is wound around the core, and `N_(2)` the number of times the second wire is wound around the core. Find the mutual inductance of the two solenoids, neglecting the end effects.

Explanation

To find the mutual inductance \( M \) of the two solenoids wound on a common air-filled core, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Let \( l \) be the length of the core.
- Let \( A \) be the cross-sectional area of the core.
- Let \( N_1 \) be the number of turns of the first solenoid.
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