A tightly-wound, long solenoid having 50 turns `cm^(-1)`, carris a current of `4.00 A`. Find the magnetic intensity `H` and the magnetic field `B` at the centre of the solenoid. What will be the values of these quantities if an iron core is inserted in the solenoid and the magnetization `I` in the core is `4.00 xx 10^6 A m^(-1)` ?

Explanation

To solve the problem, we need to find the magnetic intensity \( H \) and the magnetic field \( B \) at the center of a tightly-wound solenoid, and then determine the values of these quantities when an iron core is inserted.

### Step-by-Step Solution:

**Step 1: Calculate the Magnetic Intensity \( H \)**

The magnetic intensity \( H \) inside a solenoid is given by the formula:
\[
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