Electromagnetic wave is travelling in a medium of relative permittivity 2.25 and relative permeability 4. speed of the wave is found to be ` a xx 10^8 m//s ` what is the value of a ?

Explanation

To find the value of \( a \) in the speed of the electromagnetic wave traveling in a medium with given relative permittivity and permeability, we can follow these steps:

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

### Step 2: Substitute the given values
From the problem, we have:
- \( \epsilon_r = 2.25 \)
- \( \mu_r = 4 \)

Substituting these values into the formula:
\[ v = \frac{3 \times 10^8}{\sqrt{4 \times 2.25}} \]

### Step 3: Calculate the denominator
First, calculate \( 4 \times 2.25 \):
\[ 4 \times 2.25 = 9 \]
Now, take the square root:
\[ \sqrt{9} = 3 \]

### Step 4: Calculate the speed of the wave
Now substitute back into the equation for \( v \):
\[ v = \frac{3 \times 10^8}{3} = 10^8 \, \text{m/s} \]

### Step 5: Relate the speed to the given expression
The problem states that the speed of the wave can also be expressed as \( a \times 10^8 \, \text{m/s} \). From our calculation, we found that:
\[ v = 10^8 \, \text{m/s} \]
Thus, we can equate:
\[ a \times 10^8 = 10^8 \]

### Step 6: Solve for \( a \)
To find \( a \), we can divide both sides by \( 10^8 \):
\[ a = 1 \]

### Final Answer
The value of \( a \) is \( 1 \).

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