The magnetic susceptibility of a metrial of a rod is 299. Permeatbility of vaccum `mu_(0)`

Options

A. `3771xx10^(-7)Hm^(-1)`
B. `3771xx10^(-5)Hm^(-1)`
C. `3770xx10^(-6)Hm^(-1)`
D. `3771xx10^(-8)Hm^(-1)`

Explanation

To solve the problem, we need to find the permeability (μ) of the material given its magnetic susceptibility (χ) and the permeability of free space (μ₀).

### Step-by-Step Solution:

1. **Identify the given values:**
- Magnetic susceptibility (χ) = 299
- Permeability of vacuum (μ₀) = 4π × 10⁻⁷ H/m

2. **Use the relationship between permeability and magnetic susceptibility:**
The relationship is given by the formula:
\[ \mu_r = 1 + \chi \]
where μ_r is the relative permeability.

3. **Calculate the relative permeability (μ_r):**
Substitute the value of χ into the formula:
\[ \mu_r = 1 + 299 = 300 \]

4. **Calculate the permeability (μ):**
The permeability of the material can be calculated using the formula:
\[ \mu = \mu_r \cdot \mu_0 \]
Substitute the values of μ_r and μ₀:
\[ \mu = 300 \cdot (4\pi \times 10^{-7}) \]

5. **Perform the multiplication:**
First, calculate \(4\pi\):
\[ 4\pi \approx 12.566 \]
Now multiply:
\[ \mu \approx 300 \cdot (12.566 \times 10^{-7}) = 3.7698 \times 10^{-5} \text{ H/m} \]

6. **Convert to scientific notation:**
\[ \mu \approx 3.77 \times 10^{-5} \text{ H/m} \]

7. **Final answer:**
The permeability of the material is approximately:
\[ \mu \approx 3.77 \times 10^{-5} \text{ H/m} \]

### Conclusion:
The correct answer, rounded to significant figures, is approximately \(3.77 \times 10^{-5} \text{ H/m}\).