(a)Using Ampere's circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis.
(b )How is the magnetic field inside a given solenoid made strong?

Explanation

### Step-by-Step Solution

#### Part (a): Deriving the Expression for the Magnetic Field Inside a Long Solenoid

1. **Understand the Setup**:
- Consider a long solenoid with \( n \) turns per unit length, carrying a current \( I \).
- We want to find the magnetic field \( B \) at a point inside the solenoid along its axis.

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