Express velocity of electromagnetic wave in a material medium in terms of `mu` and `epsi`.

Options

A. ` ( epsilon_(0) mu_(0) )^(-1//2)`
B. `( epsilon_(0) e_(r) mu_(0) mu_(r) )^(-1//2)`
C. `3 xx 10^(8)` m/s
D. `((epsilon_(0) epsilon_(r) ) /(mu_(0) mu_(r) ))^(+1//2)`

Answer

To express the velocity of electromagnetic waves in a material medium in terms of permeability (μ) and permittivity (ε), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**: The speed of electromagnetic waves (V) in a medium is influenced by the medium's electric permittivity (ε) and magnetic permeability (μ). The fundamental relationship is given by:
\[ V = \frac{1}{\sqrt{\mu \cdot \epsilon}} \]

2. **Defining Relative Permittivity and Permeability**: In a material medium, the permittivity (ε) and permeability (μ) can be expressed in terms of their relative values:
- Relative permittivity:
\[ \epsilon_r = \frac{\epsilon}{\epsilon_0} \]
- Relative permeability:
\[ \mu_r = \frac{\mu}{\mu_0} \]
where ε₀ is the permittivity of free space and μ₀ is the permeability of free space.

3. **Substituting Relative Values**: We can substitute ε and μ in the velocity equation:
\[ \epsilon = \epsilon_r \cdot \epsilon_0 \]
\[ \mu = \mu_r \cdot \mu_0 \]

4. **Rewriting the Velocity Equation**: Substitute these expressions into the velocity formula:
\[ V = \frac{1}{\sqrt{\mu_r \cdot \mu_0 \cdot \epsilon_r \cdot \epsilon_0}} \]

5. **Final Expression**: Thus, the velocity of electromagnetic waves in a material medium can be expressed as:
\[ V = \frac{1}{\sqrt{\mu_r \cdot \epsilon_r \cdot \mu_0 \cdot \epsilon_0}} \]