Intensity of electromagnetic wave will be

Options

A. `I=cmu_(0)B_(0)^(2)//2`
B. `I=c epsilon_(0)B_(0)^(2)//2`
C. `I=B_(0)^(2)//cmu_(0)`
D. `I=E_(0)^(2)//2cepsilon_(0)`

Answer

To find the intensity of an electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electromagnetic Waves**:
- Electromagnetic waves consist of oscillating electric (E) and magnetic (B) fields that propagate through space. The electric field vector (E) and the magnetic field vector (B) are perpendicular to each other and also to the direction of wave propagation.

2. **Direction of Propagation**:
- The direction of propagation of the electromagnetic wave is represented by the wave vector (k). The relationship between the electric field (E), magnetic field (B), and the wave vector (k) can be expressed as:
\[ E \times B = c \]
where \(c\) is the speed of light.

3. **Defining Intensity**:
- The intensity (I) of an electromagnetic wave is defined as the average power per unit area carried by the wave. It can be calculated using the Poynting vector (S), which is given by:
\[ S = \frac{1}{\mu_0} (E \times B) \]
The intensity is the time average of this Poynting vector over one cycle.

4. **Calculating Intensity**:
- The average intensity (I) can be expressed in terms of the electric field (E) as:
\[ I = \langle S \rangle = \frac{E^2}{2 \mu_0 c} \]
where \( \mu_0 \) is the permeability of free space and \( c \) is the speed of light.

5. **Using the Relationship Between E and B**:
- The relationship between the electric field and magnetic field in an electromagnetic wave is given by:
\[ B = \frac{E}{c} \]
Using this, we can also express intensity in terms of the magnetic field (B):
\[ I = \frac{B^2 c}{2 \mu_0} \]

6. **Final Formulas**:
- Therefore, the intensity of an electromagnetic wave can be expressed in two forms:
\[ I = \frac{E^2}{2 \mu_0 c} \quad \text{(in terms of electric field)} \]
\[ I = \frac{B^2 c}{2 \mu_0} \quad \text{(in terms of magnetic field)} \]

### Summary:
The intensity of an electromagnetic wave can be calculated using the electric field or magnetic field components, leading to the formulas:
- \( I = \frac{E^2}{2 \mu_0 c} \)
- \( I = \frac{B^2 c}{2 \mu_0} \)