A solenoid of length 50cm with 20 turns per centimetre and area of cross-section 40cm? completely surrounds another coaxial solenoid of the same length, area of cross-section `25cm^(2)` with 25 turns per centimetre. Calculate the mutual inductance of the system.

Explanation

To calculate the mutual inductance of the system consisting of two coaxial solenoids, we will follow these steps:

### Step 1: Identify the given values
- Length of both solenoids, \( l = 50 \, \text{cm} = 0.5 \, \text{m} \)
- Number of turns per centimeter for the outer solenoid, \( n_1 = 20 \, \text{turns/cm} = 2000 \, \text{turns/m} \)
- Area of cross-section of the outer solenoid, \( A_1 = 40 \, \text{cm}^2 = 40 \times 10^{-4} \, \text{m}^2 \)
- Number of turns per centimeter for the inner solenoid, \( n_2 = 25 \, \text{turns/cm} = 2500 \, \text{turns/m} \)
- Area of cross-section of the inner solenoid, \( A_2 = 25 \, \text{cm}^2 = 25 \times 10^{-4} \, \text{m}^2 \)
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