The magnetic susceptibility of a rod is `499`. The absolute permeability of vacuum is `4pixx10^(-7)H//m`. The absolute permeability of the material of the rod is

Options

A. `pixx10^(-4)`
B. `2pixx10^(-4)`
C. `3pixx10^(-4)`
D. `4pixx10^(-4)`

Answer

To find the absolute permeability of the material of the rod given its magnetic susceptibility and the absolute permeability of vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Magnetic susceptibility (χ) = 499
- Absolute permeability of vacuum (μ₀) = \(4\pi \times 10^{-7} \, \text{H/m}\)

2. **Use the Formula for Absolute Permeability**:
The absolute permeability (μ) of a material is related to the absolute permeability of vacuum and the magnetic susceptibility by the formula:
\[ \mu = \mu_0 (1 + \chi) \]

3. **Substitute the Values into the Formula**:
Substitute the values of μ₀ and χ into the formula:
\[ \mu = (4\pi \times 10^{-7}) (1 + 499) \]

4. **Calculate \(1 + \chi\)**:
\[ 1 + 499 = 500 \]

5. **Multiply to Find μ**:
Now substitute this back into the equation:
\[ \mu = (4\pi \times 10^{-7}) \times 500 \]

6. **Perform the Multiplication**:
\[ \mu = 2000\pi \times 10^{-7} \, \text{H/m} \]

7. **Express in Standard Form**:
To express this in a more standard form:
\[ \mu = 2\pi \times 10^{-4} \, \text{H/m} \]

8. **Final Result**:
Thus, the absolute permeability of the material of the rod is:
\[ \mu = 2\pi \times 10^{-4} \, \text{H/m} \]