In an electromagnetic wave, the electric and magnetising fields are `100 V m^(-1)` and `0.265 Am^(-1)`. The maximum energy flow is

Options

A. `26.5 Wm^(-2)`
B. `36.5 Wm^(-2)`
C. `46.7 Wm^(-2)`
D. None of these

Explanation

To find the maximum energy flow in an electromagnetic wave, we can use the Poynting vector, which is defined as:

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

Where:
- \( S \) is the Poynting vector (energy flow per unit area),
- \( E \) is the electric field,
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space.

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

### Step 1: Convert the magnetic field \( H \) to \( B \)

The magnetic field \( B \) can be calculated using the relation:

\[ B = \mu_0 \times H \]

Where \( \mu_0 \) (the permeability of free space) is approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \).

Substituting the values:

\[ B = (4\pi \times 10^{-7}) \times 0.265 \]

Calculating \( B \):

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

### Step 2: Calculate the maximum energy flow

Using the Poynting vector formula for maximum energy flow:

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

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

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

Calculating \( S \):

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

Using \( \pi \approx 3.14 \):

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

### Step 3: Round the answer

The maximum energy flow can be rounded to:

\[ S \approx 26.5 \, \text{W/m}^2 \]

Thus, the maximum energy flow is approximately \( 26.5 \, \text{W/m}^2 \).

### Final Answer:
The maximum energy flow is \( 26.5 \, \text{W/m}^2 \).

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