The velocity of electromagnetic waves in a dieclectric medium `(epsilon_(r)=4)` is:

Options

A. `3xx10^(8) metre//second`
B. `1.5xx10^(8) metre//second`
C. `6xx10^(8) metre//second`
D. `7.5xx10^(7) metre//second`

Explanation

To find the velocity of electromagnetic waves in a dielectric medium with a dielectric constant \( \epsilon_r = 4 \), we can follow these steps:

### Step 1: Understand the relationship between the speed of light in vacuum and in a dielectric medium.
The speed of light in vacuum, denoted as \( c \), is approximately \( 3 \times 10^8 \) meters per second. When electromagnetic waves travel through a dielectric medium, their speed \( v \) is given by the equation:

\[ v = \frac{c}{\sqrt{\epsilon_r}} \]

### Step 2: Substitute the value of the dielectric constant.
Given that the dielectric constant \( \epsilon_r = 4 \), we can substitute this value into the equation:

\[ v = \frac{c}{\sqrt{4}} \]

### Step 3: Calculate the square root of the dielectric constant.
The square root of \( 4 \) is \( 2 \):

\[ \sqrt{4} = 2 \]

### Step 4: Substitute \( c \) and calculate \( v \).
Now we can substitute \( c \) into the equation:

\[ v = \frac{3 \times 10^8 \, \text{m/s}}{2} \]

### Step 5: Perform the division.
Now, we divide \( 3 \times 10^8 \) by \( 2 \):

\[ v = 1.5 \times 10^8 \, \text{m/s} \]

### Step 6: Conclusion.
Thus, the velocity of electromagnetic waves in the dielectric medium with \( \epsilon_r = 4 \) is:

\[ v = 1.5 \times 10^8 \, \text{m/s} \]

### Final Answer:
The correct answer is \( 1.5 \times 10^8 \, \text{m/s} \).

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