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

Explanation

To calculate the mutual inductance of the system 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 in the outer solenoid, \( n_1 = 20 \, \text{turns/cm} = 2000 \, \text{turns/m} \)
- Cross-sectional area of the outer solenoid, \( A_1 = 40 \, \text{cm}^2 = 40 \times 10^{-4} \, \text{m}^2 = 4 \times 10^{-3} \, \text{m}^2 \)
- Number of turns in the inner solenoid, \( n_2 = 25 \, \text{turns/cm} = 2500 \, \text{turns/m} \)
- Cross-sectional area of the inner solenoid, \( A_2 = 25 \, \text{cm}^2 = 25 \times 10^{-4} \, \text{m}^2 = 2.5 \times 10^{-3} \, \text{m}^2 \)
...