For any E.M. wave if `E = 100 V/m and B = 3.33 x10^(–7)` T. Then the rate of energy flow per unit area is

Options

A. ` 3.33 x10^(–5) J//m^(2)`
B. `26.5 VA/m^(2)`
C. `3 x10^(8) J//m^(2)`
D. None of these

Answer

To find the rate of energy flow per unit area for the given electromagnetic wave, we can use the Poynting vector \( S \), which is defined as:

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

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

Given:
- \( E = 100 \, \text{V/m} \)
- \( B = 3.33 \times 10^{-7} \, \text{T} \)

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

Using the formula for the Poynting vector:

\[ S = E \cdot B \]

Since the electric field \( E \) and magnetic field \( B \) are perpendicular to each other, we can directly multiply their magnitudes:

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

### Step 2: Substitute the values

Substituting the known values into the equation:

\[ S = \frac{100 \, \text{V/m} \cdot 3.33 \times 10^{-7} \, \text{T}}{4\pi \times 10^{-7} \, \text{T m/A}} \]

### Step 3: Calculate \( \mu_0 \)

The value of \( \mu_0 \) is:

\[ \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \approx 1.2566 \times 10^{-6} \, \text{T m/A} \]

### Step 4: Perform the calculation

Now we can calculate \( S \):

\[ S = \frac{100 \cdot 3.33 \times 10^{-7}}{1.2566 \times 10^{-6}} \]

Calculating the numerator:

\[ 100 \cdot 3.33 \times 10^{-7} = 3.33 \times 10^{-5} \]

Now divide by \( 1.2566 \times 10^{-6} \):

\[ S = \frac{3.33 \times 10^{-5}}{1.2566 \times 10^{-6}} \approx 26.5 \, \text{W/m}^2 \]

### Final Answer

Thus, the rate of energy flow per unit area is approximately:

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