Relative permitivity and permeability of a material `epsilon_(r) and mu_(r)`, respectively . Which of the following values of these quantities are allowed for a diamagnetic material?

Options

A. `epsi_(r) = 0.5, mu_(r) = 1.5`
B. `epsi_(r) = 1.5 , mu_(r) = 0.5`
C. `epsi_(r) = 0.5, mu_(r) = 0.5`
D. `epsi_(r) = 1.5, mu_(r) = 1.5`

Answer

To determine the allowed values of relative permittivity (\( \epsilon_r \)) and relative permeability (\( \mu_r \)) for a diamagnetic material, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Diamagnetism**:
- Diamagnetic materials are characterized by their response to an external magnetic field. They have a very weak negative susceptibility to magnetic fields, which means they are repelled by a magnetic field.

2. **Properties of Diamagnetic Materials**:
- For diamagnetic materials, the relative permeability (\( \mu_r \)) is always less than 1. This indicates that they do not enhance the magnetic field within them.
- The relative permittivity (\( \epsilon_r \)) can vary, but it is generally higher compared to other materials.

3. **Analyzing the Options**:
- We need to find options where \( \mu_r < 1 \) and \( \epsilon_r \) is relatively high.
- Let's consider the options provided:
- Option A: \( \epsilon_r = 0.5, \mu_r = 0.5 \)
- Option B: \( \epsilon_r = 1.5, \mu_r = 0.5 \)
- Option C: \( \epsilon_r = 1.0, \mu_r = 1.0 \)
- Option D: \( \epsilon_r = 2.0, \mu_r = 1.5 \)

4. **Evaluating Each Option**:
- **Option A**: \( \epsilon_r = 0.5 \) (not high) and \( \mu_r = 0.5 \) (valid for diamagnetic).
- **Option B**: \( \epsilon_r = 1.5 \) (high) and \( \mu_r = 0.5 \) (valid for diamagnetic).
- **Option C**: \( \epsilon_r = 1.0 \) (not high) and \( \mu_r = 1.0 \) (not valid for diamagnetic).
- **Option D**: \( \epsilon_r = 2.0 \) (high) and \( \mu_r = 1.5 \) (not valid for diamagnetic).

5. **Conclusion**:
- The only option that satisfies both conditions (high \( \epsilon_r \) and \( \mu_r < 1 \)) is **Option B**: \( \epsilon_r = 1.5 \) and \( \mu_r = 0.5 \).

### Final Answer:
**Option B**: \( \epsilon_r = 1.5 \) and \( \mu_r = 0.5 \) is allowed for a diamagnetic material.