A capacitor of capacitance `100 mu F` is connected to a battery of 20 volts for a long time and then disconnected from it. It is now connected across a long solenoid having 4000 turns per meter. It is found that the potential difference across the capacitor drops to `90^@` of its maximum value in 2.0 seconds. Estimate the average magnetic field produced at the centre of the solenoid during this period.

Explanation

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Identify the given values
- Capacitance, \( C = 100 \, \mu F = 100 \times 10^{-6} \, F \)
- Voltage, \( V = 20 \, V \)
- Turns per meter of the solenoid, \( n = 4000 \, turns/m \)
- Time, \( t = 2 \, s \)

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