In an electromagnetic wave, the electric and magnetizing field are `100V//m` and `0.265 A//m`. The maximum energy flow is:

Options

A. `26.5W//m^(2)`
B. `36.5W//m^(2)`
C. `46.7W//m^(2)`
D. `76.5W//m^(2)`

Explanation

To find the maximum energy flow in an electromagnetic wave, we can use the Poynting vector, which represents the power per unit area carried by the wave. The formula for the Poynting vector \( S \) is given by:

\[ S = \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B} \]

Where:
- \( S \) is the Poynting vector (energy flow per unit area),
- \( \mu_0 \) is the permeability of free space (approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \)),
- \( \mathbf{E} \) is the electric field,
- \( \mathbf{B} \) is the magnetic field.

Given:
- The electric field \( E = 100 \, \text{V/m} \),
- The magnetic intensity \( H = 0.265 \, \text{A/m} \).

First, we need to find the magnetic field \( B \) using the relationship:

\[ B = \mu_0 H \]

### Step 1: Calculate \( B \)

Substituting the value of \( H \):

\[ B = (4\pi \times 10^{-7} \, \text{T m/A}) \times (0.265 \, \text{A/m}) \]

Calculating \( B \):

\[ B \approx 4\pi \times 10^{-7} \times 0.265 \approx 3.51 \times 10^{-7} \, \text{T} \]

### Step 2: Calculate the Poynting vector \( S \)

Now we can calculate the Poynting vector \( S \):

\[ S = \frac{1}{\mu_0} \cdot E \cdot B \]

Substituting the values of \( E \) and \( B \):

\[ S = \frac{1}{4\pi \times 10^{-7}} \cdot (100) \cdot (3.51 \times 10^{-7}) \]

Calculating \( S \):

\[ S = \frac{100 \cdot 3.51 \times 10^{-7}}{4\pi \times 10^{-7}} \approx \frac{351 \times 10^{-7}}{4\pi \times 10^{-7}} = \frac{351}{4\pi} \]

Using \( \pi \approx 3.14 \):

\[ S \approx \frac{351}{12.56} \approx 27.94 \, \text{W/m}^2 \]

### Final Result

The maximum energy flow (Poynting vector) is approximately:

\[ S \approx 27.94 \, \text{W/m}^2 \]