Define self -inductance and its `S.I.` unit. Derive an expression for self- industance of a long, air-cored solenoid of length , radius `r`, and having `N` number of turns.

Explanation

### Step-by-Step Solution

**Step 1: Define Self-Inductance**
Self-inductance (L) of a coil is defined as the induced electromotive force (EMF) in the coil when the current flowing through it changes at a unit rate. Mathematically, it is given by:
\[ L = -\frac{d\Phi}{dt} \cdot \frac{1}{\frac{dI}{dt}} \]
where \( \Phi \) is the magnetic flux through the coil, and \( I \) is the current.

**Step 2: SI Unit of Self-Inductance**
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