There is one tightly wound long solenoid carrying current 2 A. Solenoid have 100 turns per cm. `H_1` is the magnetic intensity and `B_1` is the magnetic field at the centre of solenoid. Now an iron core is inserted inside the solenoid. Intensity of magnetization in the core is `4 xx 10^6` A/m. New values of magnetic intensity and magnetic field at the centre becomes `H_2` and `B_2`
Value of `H_2//H_1 ` is

Options

A. infinity
B. `4 xx 10^6`
C. `2 xx 10^3`
D. 1

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Magnetic Intensity (H1) of the Solenoid
The magnetic intensity \( H_1 \) in a solenoid is given by the formula:
\[ H_1 = n \cdot I \]
Where:
- \( n \) is the number of turns per meter
- \( I \) is the current in amperes

Given:
- The solenoid has 100 turns per cm, which can be converted to turns per meter:
\[ n = 100 \, \text{turns/cm} = 100 \times 100 = 10,000 \, \text{turns/m} \]
- The current \( I = 2 \, \text{A} \)

Now substituting the values:
\[ H_1 = 10,000 \, \text{turns/m} \times 2 \, \text{A} = 20,000 \, \text{A/m} = 2 \times 10^4 \, \text{A/m} \]

### Step 2: Calculate the Magnetic Field (B1) at the Center of the Solenoid
The magnetic field \( B_1 \) at the center of the solenoid is given by:
\[ B_1 = \mu_0 H_1 \]
Where \( \mu_0 \) (the permeability of free space) is:
\[ \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \]
Substituting the value of \( H_1 \):
\[ B_1 = 4\pi \times 10^{-7} \, \text{T m/A} \times 2 \times 10^4 \, \text{A/m} \]
Calculating this:
\[ B_1 = 8\pi \times 10^{-3} \, \text{T} \]

### Step 3: Determine the New Magnetic Intensity (H2) After Inserting the Iron Core
When an iron core is inserted into the solenoid, the magnetic intensity \( H \) remains unchanged. Therefore:
\[ H_2 = H_1 = 2 \times 10^4 \, \text{A/m} \]

### Step 4: Calculate the Ratio \( \frac{H_2}{H_1} \)
Since \( H_2 \) remains the same as \( H_1 \):
\[ \frac{H_2}{H_1} = \frac{H_1}{H_1} = 1 \]

### Final Answer
Thus, the value of \( \frac{H_2}{H_1} \) is:
\[ \boxed{1} \]

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