The permittivity and permeability of free space are `epsilon_(0) = 8.85 xx 10^(-12)C^(2)N^(-1)m^(-2)"and"mu_(0) = 4pi xx 10^(-7)"TmA"^(-1),` respectively. Find the velocity of the electromagnetic wave.

Answer

To find the velocity of electromagnetic waves in free space, we can use the formula:

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

where:
- \( c \) is the speed of light in vacuum (or the velocity of electromagnetic waves),
- \( \mu_0 \) is the permeability of free space,
- \( \epsilon_0 \) is the permittivity of free space.

### Step-by-Step Solution:

1. **Identify the values of permittivity and permeability**:
- Given:
\[ \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \]
\[ \mu_0 = 4\pi \times 10^{-7} \, \text{TmA}^{-1} \]

2. **Substitute the values into the formula**:
- We need to calculate \( \mu_0 \epsilon_0 \):
\[ \mu_0 \epsilon_0 = (4\pi \times 10^{-7}) \times (8.85 \times 10^{-12}) \]

3. **Calculate \( \mu_0 \epsilon_0 \)**:
- First, calculate \( 4\pi \):
\[ 4\pi \approx 12.5664 \]
- Now multiply:
\[ \mu_0 \epsilon_0 = 12.5664 \times 10^{-7} \times 8.85 \times 10^{-12} \]
\[ \mu_0 \epsilon_0 \approx 1.113 \times 10^{-18} \, \text{Tm}^2\text{C}^2\text{N}^{-1}\text{m}^{-2} \]

4. **Calculate the square root of \( \mu_0 \epsilon_0 \)**:
- Now, find the square root:
\[ \sqrt{\mu_0 \epsilon_0} = \sqrt{1.113 \times 10^{-18}} \approx 1.054 \times 10^{-9} \]

5. **Calculate the velocity \( c \)**:
- Finally, substitute back into the formula for \( c \):
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \approx \frac{1}{1.054 \times 10^{-9}} \approx 2.997 \times 10^{8} \, \text{m/s} \]

### Conclusion:
The velocity of electromagnetic waves in free space is approximately:
\[ c \approx 3.00 \times 10^{8} \, \text{m/s} \]

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