A sample of cast iron exhibits a magnetic field (B) of 0.5 T when the magnetic field intensity is `H=10A//m`. What would be the field in air for this value of H?

Options

A. `0.5xx10^-6T`
B. `4pixx10^-6T`
C. `15xx10^-2T`
D. `11.5xx10^-2m`

Answer

To find the magnetic field (B) in air for a given magnetic field intensity (H), we can use the relationship between B, H, and the permeability of free space (μ₀). The formula is given by:

\[ B = \mu_0 H \]

Where:
- \( B \) is the magnetic field in tesla (T),
- \( \mu_0 \) is the permeability of free space, which is approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \),
- \( H \) is the magnetic field intensity in amperes per meter (A/m).

### Step-by-Step Solution:

1. **Identify the given values**:
- Magnetic field intensity, \( H = 10 \, \text{A/m} \)
- Permeability of free space, \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \)

2. **Substitute the values into the formula**:
\[ B = \mu_0 H = (4\pi \times 10^{-7} \, \text{T m/A}) \times (10 \, \text{A/m}) \]

3. **Calculate the magnetic field (B)**:
\[ B = 4\pi \times 10^{-6} \, \text{T} \]

4. **Approximate the value of \( \pi \)**:
Using \( \pi \approx 3.14 \):
\[ B \approx 4 \times 3.14 \times 10^{-6} \, \text{T} \approx 12.56 \times 10^{-6} \, \text{T} \approx 1.256 \times 10^{-5} \, \text{T} \]

5. **Conclusion**:
The magnetic field in air for the given value of H is approximately \( 12.56 \, \mu T \) (microtesla).