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 determine the correct relation between the magnitudes of the electric field (E) and the magnetic field (B) in an electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces in Electric and Magnetic Fields**:
- The force on a charge (q) in an electric field (E) is given by \( F = qE \).
- The force on a charge (q) moving with velocity (v) in a magnetic field (B) is given by \( F = qvB \).

2. **Equate the Forces**:
- Since both expressions represent the force on the same charge, we can equate them:
\[ qE = qvB \]
- Dividing both sides by \( q \) (assuming \( q \neq 0 \)):
\[ E = vB \]

3. **Express the Ratio of E and B**:
- Rearranging the equation gives us:
\[ \frac{E}{B} = v \]

4. **Relate Velocity to Speed of Light**:
- In an electromagnetic wave, the velocity \( v \) is equal to the speed of light \( c \):
\[ \frac{E}{B} = c \]
- The speed of light \( c \) is approximately \( 3 \times 10^8 \, \text{m/s} \).

5. **Express c in Terms of Permittivity and Permeability**:
- The speed of light can also be expressed in terms of the permittivity (\( \epsilon_0 \)) and permeability (\( \mu_0 \)) of free space:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]

6. **Final Relation**:
- Therefore, we can conclude that:
\[ \frac{E}{B} = c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
- This means that the ratio of the electric field to the magnetic field in an electromagnetic wave is equal to the speed of light.

### Conclusion:
The correct relation is:
\[ E = cB \]
or
\[ \frac{E}{B} = c \]