The current in an ideal, long solenoid is varied at a uniform rate of `0.02A//s`. The solenoid has 1000 turns/m and its radius is 8 cm.
(i) Consider a circle of radius 2 cm inside the solenoid with its axis coinciding with the axis of the solenoid. Write the change in the magnetic flux through this circle in 4 s.
(ii) Find the electric field induced at a point on the circumference of the circle.
(iii) Find the electric field induced at a point outside the solenoid at a distance 9 cm from its axis.

Explanation

To solve the problem step by step, we will break it down into three parts as per the question.

### Given Data:
- Rate of change of current, \( \frac{dI}{dt} = 0.02 \, \text{A/s} \)
- Number of turns per unit length of the solenoid, \( n = 1000 \, \text{turns/m} \)
- Radius of the solenoid, \( R = 8 \, \text{cm} = 0.08 \, \text{m} \)
- Radius of the circle inside the solenoid, \( r = 2 \, \text{cm} = 0.02 \, \text{m} \)
- Time interval, \( t = 4 \, \text{s} \)
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