The relative permeability is represented by `mu_(r)` and susceptibility is denoted by `chi` for a magnetic substance then for a paramagnetic substance.

Options

A. `mu_(r) gt 1 , x lt 0`
B. ` mu_(r) gt 1 , x lt 0 `
C. ` mu_(r) lt 1 x gt 0 `
D. `mu_(r) lt , x lt 0`

Answer

To solve the question regarding the relative permeability (\( \mu_r \)) and susceptibility (\( \chi \)) for a paramagnetic substance, we can follow these steps:

### Step 1: Understand the Definitions
- **Relative Permeability (\( \mu_r \))**: It is the ratio of the permeability of a substance (\( \mu \)) to the permeability of free space (\( \mu_0 \)). Mathematically, it is expressed as:
\[ \mu_r = \frac{\mu}{\mu_0} \]
- **Magnetic Susceptibility (\( \chi \))**: It is a measure of how much a material will become magnetized in an applied magnetic field. It is related to relative permeability by the equation:
\[ \chi = \mu_r - 1 \]

### Step 2: Analyze the Properties of Paramagnetic Substances
- Paramagnetic substances are characterized by their ability to be weakly attracted by a magnetic field. They do not completely block magnetic field lines but allow some to pass through.

### Step 3: Determine the Values for Paramagnetic Substances
- For paramagnetic substances, the relative permeability (\( \mu_r \)) is slightly greater than 1. A commonly accepted value is:
\[ \mu_r \approx 1.007 \]

### Step 4: Calculate the Susceptibility (\( \chi \))
- Using the relationship between susceptibility and relative permeability:
\[ \chi = \mu_r - 1 \]
- Substituting the value of \( \mu_r \):
\[ \chi = 1.007 - 1 = 0.007 \]

### Step 5: Conclusion
- Therefore, for a paramagnetic substance:
- The relative permeability \( \mu_r \) is greater than 1 (specifically, around 1.007).
- The susceptibility \( \chi \) is greater than 0 (specifically, around 0.007).

### Final Answer:
- \( \mu_r > 1 \) and \( \chi > 0 \)

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