The average intensity of electromagnetic wave is (where symbols have their usual meanings)

Options

A. `epsilon_0` ×` E^(2)_RMS × c`
B. `(B^2_RMS/ mu_0) × c`
C. `(1/2) × (epsilon_0) × E^2_RMS × c`
D. Both (A) & (B)

Answer

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

### Step 1: Understand the concept of intensity
The intensity of an electromagnetic wave is defined as the power per unit area. It can be expressed mathematically as:
\[ I = \frac{P}{A} \]
where \( I \) is the intensity, \( P \) is the power, and \( A \) is the area over which the power is distributed.

### Step 2: Relate intensity to the electric field
For electromagnetic waves, the intensity can also be expressed in terms of the electric field (E) and the speed of light (c). The average intensity \( I \) can be given by the formula:
\[ I = \frac{1}{2} \epsilon_0 c E^2 \]
where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( c \) is the speed of light in vacuum,
- \( E \) is the RMS (Root Mean Square) value of the electric field.

### Step 3: Substitute the expression for \( U \)
The energy density \( U \) of the electromagnetic wave can be expressed as:
\[ U = \frac{1}{2} \epsilon_0 E^2 \]
Thus, we can rewrite the intensity in terms of the energy density:
\[ I = c \cdot U \]

### Step 4: Final expression for average intensity
Substituting the expression for \( U \) into the intensity equation, we get:
\[ I = c \cdot \left(\frac{1}{2} \epsilon_0 E^2\right) \]
This gives us the average intensity of the electromagnetic wave in terms of the electric field.

### Conclusion
The average intensity of an electromagnetic wave is:
\[ I = \frac{1}{2} \epsilon_0 c E^2 \]