The speed of electmagnetic waves in vacuum is equal to

Options

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

Explanation

To find the speed of electromagnetic waves in a vacuum, we can use the relationship between the permeability (μ₀) and permittivity (ε₀) of free space. The speed of electromagnetic waves (c) is given by the formula:

\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]

### Step-by-Step Solution:

1. **Identify the Constants**:
- The permeability of free space (μ₀) is given as:
\[ \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \]
- The permittivity of free space (ε₀) is given as:
\[ \epsilon_0 = \frac{1}{4\pi \times 9 \times 10^9} \, \text{F/m} \]

2. **Substitute the Values**:
- We need to calculate \( \sqrt{\mu_0 \epsilon_0} \):
\[ \epsilon_0 = \frac{1}{4\pi \times 9 \times 10^9} \]
- Now, substituting the values into the formula for c:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]

3. **Calculate the Product**:
- First, calculate \( \mu_0 \epsilon_0 \):
\[ \mu_0 \epsilon_0 = (4\pi \times 10^{-7}) \times \left(\frac{1}{4\pi \times 9 \times 10^9}\right) \]
- Simplifying this gives:
\[ \mu_0 \epsilon_0 = \frac{10^{-7}}{9 \times 10^9} = \frac{10^{-16}}{9} \]

4. **Take the Square Root**:
- Now, calculate the square root:
\[ \sqrt{\mu_0 \epsilon_0} = \sqrt{\frac{10^{-16}}{9}} = \frac{10^{-8}}{3} \]

5. **Calculate the Speed**:
- Finally, substitute back into the formula for c:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = \frac{1}{\frac{10^{-8}}{3}} = 3 \times 10^8 \, \text{m/s} \]

Thus, the speed of electromagnetic waves in vacuum is:

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

### Conclusion:
The speed of electromagnetic waves in vacuum is equal to \( 3 \times 10^8 \, \text{m/s} \).