The relation between electric field E and magnetic field H in an electromagnetic wave is

Options

A. E = H
B. `E= (mu_(0))/varepsilon_(0) H`
C. `E= sqrt((mu_(0))/varepsilon_(0)) H`
D. `E= sqrt(varepsilon_(0)/(mu_(0))) H`

Answer

To find the relation between the electric field \( E \) and the magnetic field \( H \) in an electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electromagnetic Wave**:
- An electromagnetic (EM) wave consists of oscillating electric and magnetic fields that propagate through space. The electric field is denoted by \( E \) and the magnetic field intensity is denoted by \( H \).

2. **Using Maxwell's Equations**:
- Maxwell's equations describe how electric and magnetic fields interact. One of the key results from these equations is the relationship between the electric field \( E \) and the magnetic field \( B \) in an electromagnetic wave.

3. **Relating \( B \) and \( H \)**:
- The magnetic field \( B \) is related to the magnetic field intensity \( H \) by the equation:
\[ B = \mu_0 H \]
where \( \mu_0 \) is the permeability of free space.

4. **Speed of Light**:
- The speed of light \( c \) in a vacuum is given by:
\[ c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \]
where \( \epsilon_0 \) is the permittivity of free space.

5. **Relationship Between \( E \) and \( B \)**:
- From the properties of electromagnetic waves, we know that:
\[ \frac{E}{B} = c \]
Substituting \( B = \mu_0 H \) into this equation gives:
\[ \frac{E}{\mu_0 H} = c \]

6. **Solving for \( E \)**:
- Rearranging the equation gives:
\[ E = c \cdot \mu_0 H \]
Now, substituting \( c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \):
\[ E = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \cdot \mu_0 H \]

7. **Final Expression**:
- Simplifying this expression, we get:
\[ E = \sqrt{\frac{\mu_0}{\epsilon_0}} H \]
Thus, the relation between the electric field \( E \) and the magnetic field \( H \) in an electromagnetic wave is:
\[ E = \sqrt{\frac{\mu_0}{\epsilon_0}} H \]

### Conclusion:
The relation between the electric field \( E \) and the magnetic field \( H \) in an electromagnetic wave is given by:
\[ E = \sqrt{\frac{\mu_0}{\epsilon_0}} H \]