Velocity of light is equal to

Options

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

Explanation

To find the velocity of light, we can derive it from Maxwell's equations. Here’s the step-by-step solution:

### Step 1: Understanding the Relationship
The velocity of light in a vacuum can be derived from Maxwell's equations. According to these equations, electromagnetic waves propagate through a vacuum at a speed denoted by \( c \).

### Step 2: Using the Formula
The speed of light \( c \) can be expressed in terms of the permittivity \( \epsilon_0 \) and permeability \( \mu_0 \) of free space using the formula:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]

### Step 3: Identifying the Correct Expression
From the derived formula, we can see that the speed of light is inversely proportional to the square root of the product of the permeability and permittivity of free space.

### Step 4: Selecting the Right Option
Now, we need to match this expression with the options given in the question. The correct expression for the speed of light is:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
This corresponds to the option that states \( \frac{1}{\sqrt{\mu_0 \epsilon_0}} \).

### Conclusion
Thus, the velocity of light is equal to:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]