The speed of em wave in the unit of `10^8m//s`, in a medium of dielectric constant 2.25 and relative permeablity 4 is:

Options

A. `0.5 xx 10^(8)` m/s
B. `0.25 xx 10^(8)` m//s
C. `0.75 xx 10^(8)` m/s
D. `1 xx 10^(8)` m/s

Answer

To find the speed of an electromagnetic (EM) wave in a medium with a given dielectric constant and relative permeability, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Dielectric constant (\( \epsilon_r \)) = 2.25
- Relative permeability (\( \mu_r \)) = 4
- Speed of light in vacuum (\( c \)) = \( 3 \times 10^8 \, \text{m/s} \)

2. **Use the Formula for Speed of EM Wave**:
The speed of an EM wave in a medium is given by the formula:
\[ v = \frac{c}{\sqrt{\epsilon_r \cdot \mu_r}} \]

3. **Substitute the Given Values**:
Substitute the values of \( \epsilon_r \) and \( \mu_r \) into the formula:
\[ v = \frac{3 \times 10^8}{\sqrt{2.25 \cdot 4}} \]

4. **Calculate the Product Inside the Square Root**:
Calculate \( 2.25 \cdot 4 \):
\[ 2.25 \cdot 4 = 9 \]

5. **Find the Square Root**:
Now, find the square root of 9:
\[ \sqrt{9} = 3 \]

6. **Substitute Back into the Formula**:
Now substitute back into the speed formula:
\[ v = \frac{3 \times 10^8}{3} \]

7. **Simplify the Expression**:
Simplifying the expression gives:
\[ v = 1 \times 10^8 \, \text{m/s} \]

8. **Conclusion**:
The speed of the EM wave in the given medium is:
\[ v = 1 \times 10^8 \, \text{m/s} \]
Therefore, the correct answer is option 4.