The range of magnetic susceptibility and relative magnetic permeability for diamagnetic subtance are

Options

A. `-1 ge chi gt 0, 0 le mu_(r) lt 1`
B. `-1 le chi gt 0, 0 ge mu_(r) lt 1`
C. `-1 ge chi gt 1, 0 le mu_(r) lt 1`
D. `-1 le chi le 0, 0 le mu_(r) le 1`

Answer

To solve the question regarding the range of magnetic susceptibility and relative magnetic permeability for diamagnetic substances, we will follow these steps:

### Step 1: Understand Magnetic Susceptibility
Magnetic susceptibility (χ) is a measure of how much a material will become magnetized in an applied magnetic field. For diamagnetic substances, the susceptibility is negative and falls within the range:
\[ -1 < \chi \leq 0 \]

### Step 2: Relate Susceptibility to Relative Permeability
The relationship between magnetic susceptibility (χ) and relative permeability (μ_r) is given by the formula:
\[ \chi = \mu_r - 1 \]
From this equation, we can express relative permeability in terms of susceptibility:
\[ \mu_r = \chi + 1 \]

### Step 3: Substitute the Range of Susceptibility
Now, we will substitute the range of susceptibility into the equation for relative permeability:
1. Substitute the upper limit of susceptibility (χ = 0):
\[ \mu_r = 0 + 1 = 1 \]
2. Substitute the lower limit of susceptibility (χ = -1):
\[ \mu_r = -1 + 1 = 0 \]

### Step 4: Determine the Range of Relative Permeability
From the above calculations, we find that:
\[ 0 < \mu_r \leq 1 \]

### Conclusion
Thus, the ranges for diamagnetic substances are:
- **Magnetic Susceptibility (χ)**: \(-1 < \chi \leq 0\)
- **Relative Permeability (μ_r)**: \(0 < \mu_r \leq 1\)

### Final Answer
The range of magnetic susceptibility and relative magnetic permeability for diamagnetic substances is:
- **Magnetic Susceptibility (χ)**: \(-1 < \chi \leq 0\)
- **Relative Permeability (μ_r)**: \(0 < \mu_r \leq 1\)

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