If `mu` is the permeability and `epsilon` is the permittivity then `(1)/(sqrt(mu epsilon))` is equal to

Options

A. speed of sound
B. speed of light in vacuum
C. speed of sound in medium
D. speed of light in medium

Answer

To solve the problem, we need to find out what \(\frac{1}{\sqrt{\mu \epsilon}}\) represents, where \(\mu\) is the permeability and \(\epsilon\) is the permittivity of a medium.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- **Permeability (\(\mu\))**: This is a measure of how well a material can support the formation of a magnetic field within itself.
- **Permittivity (\(\epsilon\))**: This is a measure of how well a material can support the electric field within itself.

2. **Speed of Light in Vacuum**:
- The speed of light in vacuum (\(C\)) is given by the formula:
\[ C = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
where \(\mu_0\) is the permeability of free space and \(\epsilon_0\) is the permittivity of free space.

3. **Speed of Light in a Medium**:
- For a medium, the speed of light (\(V\)) can be expressed in terms of the medium's permeability and permittivity:
\[ V = \frac{1}{\sqrt{\mu \epsilon}} \]
where \(\mu\) and \(\epsilon\) are the permeability and permittivity of the medium, respectively.

4. **Relating the Two Speeds**:
- The relationship between the speed of light in vacuum and in a medium can be established using the relative permeability (\(\mu_r\)) and relative permittivity (\(\epsilon_r\)):
\[ \mu = \mu_0 \mu_r \quad \text{and} \quad \epsilon = \epsilon_0 \epsilon_r \]

5. **Substituting into the Speed Formula**:
- By substituting \(\mu\) and \(\epsilon\) into the speed of light formula for a medium, we get:
\[ V = \frac{1}{\sqrt{\mu_0 \mu_r \epsilon_0 \epsilon_r}} \]

6. **Conclusion**:
- Thus, we conclude that \(\frac{1}{\sqrt{\mu \epsilon}}\) represents the speed of light in a medium, which can be denoted as \(V\).

### Final Answer:
\[ \frac{1}{\sqrt{\mu \epsilon}} = V \quad \text{(Speed of light in the medium)} \]