The velocity of electromagnetic waves in free space can be given by relation........

Options

A. `sqrt(mu_(0)epsi_(0))`
B. `sqrt((mu_(0))/(epsi_(0)))`
C. `sqrt((epsi_(0))/(mu_(0)))`
D. `sqrt(1)/(sqrt(mu_(0)epsi_(0)))`

Explanation

To find the velocity of electromagnetic waves in free space, we can use the relationship involving the permittivity and permeability of free space. Here’s a step-by-step solution:

### Step 1: Understand the Constants
- The permeability of free space (μ₀) is given as:
\[ \mu_0 = 4\pi \times 10^{-7} \, \text{N/A}^2 \]
- The permittivity of free space (ε₀) is given as:
\[ \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \]

### Step 2: Write the Formula for Velocity
The velocity (C) of electromagnetic waves in free space is given by the formula:
\[ C = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \]

### Step 3: Substitute the Values
Now, substitute the values of ε₀ and μ₀ into the formula:
\[ C = \frac{1}{\sqrt{(8.85 \times 10^{-12}) (4\pi \times 10^{-7})}} \]

### Step 4: Calculate the Product
First, calculate the product of ε₀ and μ₀:
\[ \epsilon_0 \mu_0 = (8.85 \times 10^{-12}) \times (4\pi \times 10^{-7}) \]
Using the approximation for π (π ≈ 3.14):
\[ \epsilon_0 \mu_0 \approx (8.85 \times 10^{-12}) \times (4 \times 3.14 \times 10^{-7}) \approx (8.85 \times 10^{-12}) \times (1.256 \times 10^{-6}) \approx 1.11 \times 10^{-17} \]

### Step 5: Take the Square Root
Now, take the square root of the product:
\[ \sqrt{\epsilon_0 \mu_0} \approx \sqrt{1.11 \times 10^{-17}} \approx 1.05 \times 10^{-8} \]

### Step 6: Calculate the Velocity
Now, calculate the velocity:
\[ C = \frac{1}{1.05 \times 10^{-8}} \approx 3 \times 10^{8} \, \text{m/s} \]

### Conclusion
Thus, the velocity of electromagnetic waves in free space is approximately:
\[ C \approx 3 \times 10^8 \, \text{m/s} \]

### Final Answer
The velocity of electromagnetic waves in free space can be expressed as:
\[ C = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \approx 3 \times 10^8 \, \text{m/s} \]

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