Which of the following relation is correct?

Options

A. `sqrt(epsi_(0))E_(0) = sqrt(mu_(0))B_(0)`
B. `sqrt(mu_(0)epsi_(0)) = B_(0)//E_(0)`
C. `E_(0) = sqrt(mu_(0)epsi_(0))B_(0)`
D. `sqrt(epsi_(0))E_(0) = sqrt(epsi_(0))B_(0)`

Explanation

To solve the problem of establishing the correct relation among \( E_0 \), \( V_0 \), \( \mu_0 \), and \( \epsilon_0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the relationship in electromagnetic waves**:
In electromagnetic waves, the ratio of the amplitude of the electric field (\( E_0 \)) to the amplitude of the magnetic field (\( V_0 \)) is constant and equal to the speed of light (\( C \)). This can be expressed as:
\[ \frac{E_0}{V_0} = C \]

2. **Expressing the speed of light**:
The speed of light in a vacuum is given by the equation:
\[ C = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
where \( \mu_0 \) is the permeability of free space and \( \epsilon_0 \) is the permittivity of free space.

3. **Relating \( E_0 \) and \( V_0 \) to \( \mu_0 \) and \( \epsilon_0 \)**:
From the first equation, we can rearrange it to express \( E_0 \) in terms of \( V_0 \):
\[ E_0 = C \cdot V_0 \]

4. **Substituting the expression for \( C \)**:
Now, substituting the expression for \( C \) into the equation gives:
\[ E_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \cdot V_0 \]

5. **Rearranging the equation**:
Rearranging the equation to find the relationship between \( E_0 \), \( V_0 \), \( \mu_0 \), and \( \epsilon_0 \):
\[ \frac{E_0}{V_0} = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
Taking the reciprocal of both sides gives:
\[ \frac{V_0}{E_0} = \sqrt{\mu_0 \epsilon_0} \]

6. **Identifying the correct option**:
Based on the derived relation, we can conclude that the correct relation among the given options is:
\[ V_0 = E_0 \sqrt{\mu_0 \epsilon_0} \]
Therefore, if option 2 states this relation, it is the correct answer.

### Conclusion:
The correct relation is \( V_0 = E_0 \sqrt{\mu_0 \epsilon_0} \) (assuming option 2 corresponds to this).