a. Calculate the inductance of an air core solenoid containing `300` turns if the length of the solenoid is `25.0cm` and its cross -sectional area is `4.00cm^2`.
b. Calculate the self -induced emf in the solenoid if the current through it is decreasing at the rate of `50.0A//s`.

Explanation

To solve the problem step by step, we will break it down into two parts: (a) calculating the inductance of the solenoid and (b) calculating the self-induced emf in the solenoid.

### Part (a): Calculate the Inductance of the Solenoid

1. **Identify Given Values:**
- Number of turns, \( N = 300 \)
- Length of the solenoid, \( l = 25.0 \, \text{cm} = 0.25 \, \text{m} \)
- Cross-sectional area, \( A = 4.00 \, \text{cm}^2 = 4.00 \times 10^{-4} \, \text{m}^2 \)
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