The susceptibility of a substance in vacuum is

Options

A. One
B. Zero
C. Infinite
D. Depends upon the nature of substance

Answer

To solve the question regarding the susceptibility of a substance in a vacuum, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Susceptibility**:
- The susceptibility (χ) of a substance is a measure of how much it will become magnetized in an applied magnetic field. It is defined as:
\[ \chi = \mu_r - 1 \]
where \( \mu_r \) is the relative permeability of the substance.

2. **Defining Relative Permeability**:
- The relative permeability (\( \mu_r \)) is defined as the ratio of the permeability of the substance (\( \mu \)) to the permeability of free space (\( \mu_0 \)):
\[ \mu_r = \frac{\mu}{\mu_0} \]

3. **Considering Vacuum**:
- In a vacuum, the permeability (\( \mu \)) is equal to the permeability of free space (\( \mu_0 \)). Therefore:
\[ \mu = \mu_0 \]

4. **Calculating Relative Permeability in Vacuum**:
- Substituting this into the equation for relative permeability:
\[ \mu_r = \frac{\mu_0}{\mu_0} = 1 \]

5. **Finding Susceptibility in Vacuum**:
- Now, substituting \( \mu_r \) back into the susceptibility formula:
\[ \chi = \mu_r - 1 = 1 - 1 = 0 \]

6. **Conclusion**:
- Therefore, the susceptibility of a substance in a vacuum is:
\[ \chi = 0 \]

### Final Answer:
The susceptibility of a substance in vacuum is **0**.