An iron rod of length 20 cm and diameter 1 cm is placed inside a solenoid on which the number of turns is 600.The relative permeability of the rod is 1000.If a current of 0.5 A ios placed in the solenoid,then magnetisation of the rod will be

Options

A. `2.997xx10^(2) A/m`
B. `2.9979xx10^(3)A/m`
C. `2.997 xx10^(4) A/m`
D. `2.997 xx 10^(5) A/m`

Explanation

To find the magnetization of the iron rod placed inside a solenoid, we will follow these steps:

### Step 1: Identify Given Values
- Length of the iron rod (L) = 20 cm = 0.2 m
- Diameter of the iron rod (d) = 1 cm = 0.01 m
- Radius of the iron rod (r) = d/2 = 0.005 m
- Number of turns in the solenoid (N) = 600
- Current (I) = 0.5 A
- Relative permeability of the rod (μ_r) = 1000

### Step 2: Calculate the Magnetizing Field (H)
The magnetizing field (H) in a solenoid is given by the formula:
\[ H = \frac{N \cdot I}{L} \]
Where:
- N = number of turns
- I = current
- L = length of the solenoid (in meters)

Substituting the values:
\[ H = \frac{600 \cdot 0.5}{0.2} \]
\[ H = \frac{300}{0.2} = 1500 \, \text{A/m} \]

### Step 3: Calculate Magnetic Susceptibility (χ)
The magnetic susceptibility (χ) is related to the relative permeability (μ_r) by the formula:
\[ \chi = \mu_r - 1 \]
Substituting the given value of μ_r:
\[ \chi = 1000 - 1 = 999 \]

### Step 4: Calculate the Magnetization (M)
The magnetization (M) of the material can be calculated using the formula:
\[ M = \chi \cdot H \]
Substituting the values:
\[ M = 999 \cdot 1500 \]
\[ M = 1498500 \, \text{A/m} \]

### Step 5: Convert to Scientific Notation
To express the result in scientific notation:
\[ M = 1.4985 \times 10^6 \, \text{A/m} \]

### Final Answer
The magnetization of the rod is approximately:
\[ M \approx 1.4985 \times 10^6 \, \text{A/m} \]

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