The speed of light in vacuum is equal to

Options

A. `mu_0epsilon_0`
B. `sqrt(mu_0epsilon_0)`
C. `1/(mu_0epsilon_0)`
D. `1/(sqrt(mu_0epsilon_0))`

Answer

To solve the question regarding the speed of light in a vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**: The speed of light in a vacuum is a fundamental constant in physics. It is denoted by the letter 'C'.

2. **Referencing Maxwell's Equations**: According to Maxwell's equations, the speed of electromagnetic waves (which includes light) in a vacuum is determined by two physical constants: the permeability of free space (μ₀) and the permittivity of free space (ε₀).

3. **Formula for Speed of Light**: The speed of light in a vacuum can be expressed using the formula:
\[ C = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
where:
- \(C\) is the speed of light in vacuum,
- \(\mu_0\) is the permeability of free space (approximately \(4\pi \times 10^{-7} \, \text{T m/A}\)),
- \(\epsilon_0\) is the permittivity of free space (approximately \(8.85 \times 10^{-12} \, \text{F/m}\)).

4. **Calculating the Speed of Light**: Plugging in the values of \(\mu_0\) and \(\epsilon_0\) into the formula gives:
\[ C = \frac{1}{\sqrt{(4\pi \times 10^{-7}) \times (8.85 \times 10^{-12})}} \]
This calculation results in:
\[ C \approx 3 \times 10^8 \, \text{m/s} \]

5. **Identifying the Correct Option**: In the context of the question, we need to identify which option corresponds to this value. Based on common knowledge, the speed of light in vacuum is approximately \(3 \times 10^8 \, \text{m/s}\).

6. **Conclusion**: After checking the provided options, we conclude that the correct answer is option D, which represents the speed of light in vacuum.