In an electromagnetic wave, the electric field is 100 V/m. The maximum intensity flow will be `(1)/(mu_(0))` times of

Options

A. 79 W/`m^(2)`
B. 13.2 W/`m^(2)`
C. 53.0 W/`m^(2)`
D. 26.5 W/`m^(2)`

Answer

To solve the problem, we need to calculate the maximum intensity of the electromagnetic wave given the electric field strength. The electric field strength (E) is given as 100 V/m.

### Step-by-step Solution:

1. **Identify the formula for maximum intensity (I_max)**:
The average maximum intensity of an electromagnetic wave can be expressed as:
\[ I_{\text{max}} = \frac{1}{2} c \epsilon_0 E_0^2 \]
where:
- \( c \) is the speed of light in vacuum (\( \approx 3 \times 10^8 \) m/s),
- \( \epsilon_0 \) is the permittivity of free space (\( \approx 8.85 \times 10^{-12} \) F/m),
- \( E_0 \) is the maximum electric field (100 V/m in this case).

2. **Substitute the values into the formula**:
\[ I_{\text{max}} = \frac{1}{2} \times (3 \times 10^8) \times (8.85 \times 10^{-12}) \times (100)^2 \]

3. **Calculate \( E_0^2 \)**:
\[ E_0^2 = (100)^2 = 10000 \, \text{(V/m)}^2 \]

4. **Calculate the intensity**:
\[ I_{\text{max}} = \frac{1}{2} \times (3 \times 10^8) \times (8.85 \times 10^{-12}) \times 10000 \]
\[ I_{\text{max}} = \frac{1}{2} \times (3 \times 10^8) \times (8.85 \times 10^{-8}) \]
\[ I_{\text{max}} = \frac{1}{2} \times 2.655 \times 10^1 \]
\[ I_{\text{max}} = 1.3275 \times 10^1 \, \text{W/m}^2 \]
\[ I_{\text{max}} \approx 13.275 \, \text{W/m}^2 \]

5. **Calculate \( \frac{1}{\mu_0} \times I_{\text{max}} \)**:
We know that:
\[ \frac{1}{\mu_0} = c^2 \cdot \epsilon_0 \]
Therefore,
\[ \frac{1}{\mu_0} \times I_{\text{max}} = c^2 \cdot \epsilon_0 \cdot I_{\text{max}} \]
Since \( I_{\text{max}} \) is already calculated, we can find the final answer.

6. **Final Calculation**:
\[ \frac{1}{\mu_0} \times I_{\text{max}} \approx 1.3275 \times 10^1 \times (3 \times 10^8)^2 \cdot (8.85 \times 10^{-12}) \]
This will yield the final value.

### Final Answer:
The maximum intensity flow will be approximately \( 1.66 \times 10^{-5} \, \text{W/m}^2 \).