A long solenoid of radius 4 cm, length 400 cmcarries a current of 3 A. The total number of turns is 100. Assuming ideal solenoid, find the flux passing through a circular surface having centre on axis of solenoid of radius 3 cm and is perpendicular to the axis of solenoid (i) inside and (ii) at the end of solenoid.

Explanation

To solve the problem, we need to find the magnetic flux passing through a circular surface with a radius of 3 cm, both inside the solenoid and at the end of the solenoid. We will follow these steps:

### Step 1: Convert Given Measurements to SI Units
- Radius of the solenoid, \( R = 4 \, \text{cm} = 0.04 \, \text{m} \)
- Length of the solenoid, \( L = 400 \, \text{cm} = 4 \, \text{m} \)
- Current, \( I = 3 \, \text{A} \)
- Total number of turns, \( N = 100 \)
- Radius of the circular surface, \( r = 3 \, \text{cm} = 0.03 \, \text{m} \)
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