The velocity of electromagnetic waves in a dielectric medium `(in_(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

Answer

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

### Step 1: Understand the relationship between speed, permittivity, and vacuum speed
The speed of electromagnetic waves in a medium is given by the formula:
\[ v = \frac{c}{\sqrt{\epsilon_r}} \]
where:
- \( v \) is the speed of the electromagnetic wave in the medium,
- \( c \) is the speed of electromagnetic waves in a vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( \epsilon_r \) is the relative permittivity of the medium.

### Step 2: Substitute the values into the formula
Given that \( \epsilon_r = 4 \), we can substitute this value into the formula:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{\sqrt{4}} \]

### Step 3: Calculate the square root of the relative permittivity
Calculate \( \sqrt{4} \):
\[ \sqrt{4} = 2 \]

### Step 4: Substitute the square root back into the equation
Now substitute \( \sqrt{4} \) back into the equation:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{2} \]

### Step 5: Perform the division
Now perform the division to find \( v \):
\[ v = 1.5 \times 10^8 \, \text{m/s} \]

### Step 6: Finalize the answer
Thus, the velocity of electromagnetic waves in a dielectric medium with a relative permittivity of 4 is:
\[ v = 1.5 \times 10^8 \, \text{m/s} \]

### Summary
The velocity of electromagnetic waves in a dielectric medium with relative permittivity \( \epsilon_r = 4 \) is \( 1.5 \times 10^8 \, \text{m/s} \).

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